- Staff Selection Commission Mathematics 1999 to 2017 - TIME AND WORK Part 3

# Staff Selection Commission Mathematics - TIME AND WORK TYPE-I

Ans .

(3) 10 days

1. Explanation :

(3) According to question, A and B can do a work in 12 days .
(A + B)s one days work = $$\frac{1}{12}$$ Similarly,
(B + C)s one days work = $$\frac{1}{15}$$ and (C + A)s one days work = $$\frac{1}{20}$$ .
2 (A + B + C)s one dayss work =$$\frac{1}{12}$$ +$$\frac{1}{15}$$ +$$\frac{1}{20}$$ = $$\frac{10+8+6}{120}$$ = $$\frac{1}{5}$$
=> (A + B + C)s one dayss work = $$\frac{1}{10}$$
A, B and C together can finish the whole work in 10 days.

Ans .

(3) 60 days

1. Explanation :

(3) (A+B)s 1 days work = $$\frac{1}{72}$$ .
(B+C)s 1 days work =$$\frac{1}{120}$$ and (C+A)s 1 days work = $$\frac{1}{90}$$ .
2 (A + B + C)s 1 days work =$$\frac{1}{72}$$ +$$\frac{1}{120}$$ +$$\frac{1}{90}$$ = $$\frac{5+3+4}{360}$$ = $$\frac{1}{30}$$
=>(A+B+C)s 1 days work = $$\frac{1}{60}$$
(A+B+C) will do the work in 60 days.

Ans .

(1) 4 days

1. Explanation :

(1) According to question, 10 mens one days work =$$\frac{1}{12}$$
1 man one days work =$$\frac{1}{12*10}$$ = $$\frac{1}{120}$$
Similarly, 1 woman one days work =$$\frac{1}{6*10}$$ = $$\frac{1}{60}$$
(1 man + 1 woman)s one days work =$$\frac{1}{120}$$ +$$\frac{1}{60}$$ =$$\frac{1+2}{120}$$ = $$\frac{3}{120}$$ = $$\frac{1}{40}$$
(10 men + 10 women)s one days work = $$\frac{10}{40}$$= $$\frac{1}{4}$$
Therefore, both the teams can finish the whole work in 4 days.

Ans .

(3) 3.6 days

1. Explanation :

(3) According to question, A can finish the whole work in 6 days. As one days work=$$\frac{1}{6}$$
Similarly, Bs one days work = $$\frac{1}{9}$$
(A + B)s one days work=$$\frac{1}{6}$$ +$$\frac{1}{9}$$ = $$\frac{3+2}{18}$$ +$$\frac{5}{18}$$
Therefore, (A + B)s can finish thewhole work in $$\frac{18}{5}$$ days i.e., 3.6 days. .

Ans .

(2)120 days

1. Explanation :

(2) According to the question Work done by A and B together in one day = $$\frac{1}{10}$$ part Work done by B and C together in one day = $$\frac{1}{15}$$ part Work done by C and A together in one day = $$\frac{1}{20}$$ part.
So, A + B = $$\frac{1}{10}$$ ....(I)
B + C = $$\frac{1}{15}$$ ...(II)
C + A = $$\frac{1}{20}$$ ....(III)
Adding I, II, III, we get 2 (A + B + C) = $$\frac{1}{10}$$ +$$\frac{1}{15}$$ +$$\frac{1}{20}$$
2 (A + B + C) =$$\frac{6+4+3}{60}$$ =$$\frac{13}{60}$$
A + B + C = 13 120 ....(IV)
Putting the value of eqn. (I) in eqn. (IV) $$\frac{1}{10}$$+c =$$\frac{13}{120}$$ Work done in 1 day by C is $$\frac{1}{120}$$ part.
Hence, C will finish the whole work in 120 days

Ans .

(2)12 hours

1. Explanation :

(2) As 1 hours work = $$\frac{1}{4}$$
(B + C)s 1 hours work = $$\frac{1}{3}$$ and (A + C)s 1 hours work = $$\frac{1}{2}$$
Cs 1 hours work = $$\frac{1}{2}$$ - $$\frac{1}{4}$$ = $$\frac{2-1}{4}$$ =$$\frac{1}{4}$$
and Bs 1 hours work = $$\frac{1}{3}$$ - $$\frac{1}{4}$$ = $$\frac{4-3}{12}$$ =$$\frac{1}{12}$$
Hence, B alone can do the work in 12 hours.

Ans .

(3)3$$\frac{3}{7}$$days

1. Explanation :

(3) As 1 days work =$$\frac{1}{24}$$
Bs 1 days work = $$\frac{1}{6}$$ and Cs 1 day+s work = $$\frac{1}{12}$$
(A + B + C)s 1 days work =$$\frac{1}{24}$$ + $$\frac{1}{6}$$ +$$\frac{1}{12}$$ =$$\frac{1+4+2}{24}$$ =$$\frac{7}{24}$$
The work will be completed by them in $$\frac{24}{7}$$ i.e.. 3$$\frac{3}{7}$$days.

Ans .

(3) 15 days

1. Explanation :

(3) (A + B)s 1 days work =$$\frac{1}{10}$$
As 1 days work =$$\frac{1}{30}$$
Bs 1 days work =$$\frac{1}{10}$$-$$\frac{1}{30}$$ = $$\frac{3-1}{30}$$=$$\frac{2}{30}$$=$$\frac{1}{15}$$
Hence, B, alone can complete the work in 15 days.

Ans .

(3) 120 days

1. Explanation :

(3) (A + B)s 1 days work=$$\frac{1}{72}$$
(B + C)s 1 days work =$$\frac{1}{120}$$ and (C + A)s 1 days work =$$\frac{1}{90}$$
2(A + B + C)s 1 days work =$$\frac{1}{72}$$ + $$\frac{1}{120}$$+ $$\frac{3-1}{90}$$ = $$\frac{5+3+4}{360}$$= $$\frac{12}{360}$$ =$$\frac{1}{30}$$
(A + B + C)s 1 days work =$$\frac{1}{60}$$
Now, As 1 days work = (A + B + C)s 1 days work - (B + C)s 1 days work=$$\frac{1}{60}$$-$$\frac{1}{120}$$=$$\frac{2-1}{120}$$=$$\frac{1}{120}$$ A alone can complete the work in 120 days. .

Ans .

(3) 5$$\frac{5}{47}$$days

1. Explanation :

(3) (A + B)s 1 days work $$\frac{1}{8}$$
(B + C)s 1 days work =$$\frac{1}{6}$$ and (C + A)s 1 days work =$$\frac{1}{10}$$
On adding, 2(A + B + C)s 1 days work= $$\frac{1}{8}$$+$$\frac{1}{6}$$+$$\frac{1}{10}$$
=$$\frac{15+20+12}{120}$$=$$\frac{47}{120}$$
=> (A + B + C)'s 1 days work =$$\frac{47}{240}$$.
(A + B + C) together will complete the work in $$\frac{240}{47}$$=5$$\frac{5}{47}$$ = days.

Ans .

(4)48 days

1. Explanation :

(4) (A + B)s 1 days work =$$\frac{1}{12}$$(i)
(B + C)s 1 days work=$$\frac{1}{8}$$ (ii) and (C + A)s 1 days work=$$\frac{1}{6}$$(iii)
On adding, 2(A + B + C)s 1 days work =$$\frac{1}{12}$$ +$$\frac{1}{8}$$ +$$\frac{1}{6}$$ =$$\frac{2+3+4}{24}$$ =$$\frac{9}{24}$$
(A+ B + C)'s 1 days work =$$\frac{9}{24*2}$$=$$\frac{9}{48}$$ ...(iv)
On, subtracting (iii) from (iv),
Bs 1 days work =$$\frac{9}{48}$$ -$$\frac{1}{6}$$ =$$\frac{9-8}{48}$$ =$$\frac{1}{48}$$
=> B can complete the work in 48 days.

Ans .

(4)13$$\frac{1}{3}$$days

1. Explanation :

(4) Work done by (A + B) in 1 day =$$\frac{1}{30}$$
Work done by (B + C) in 1 day = $$\frac{1}{20}$$ and Work done by (C + A) in 1 day = $$\frac{1}{15}$$
On adding, Work done by 2 (A +B + C) in 1 day =$$\frac{1}{30}$$+$$\frac{1}{20}$$+$$\frac{1}{15}$$=$$\frac{2+3+4}{60}$$=$$\frac{9}{60}$$=$$\frac{3}{20}$$
Work done by (A + B + C) in 1 day =$$\frac{3}{40}$$
(A + B + C) will do the work in $$\frac{4}{30}$$ = 13$$\frac{1}{3}$$days

Ans .

(1)8 days

1. Explanation :

(1) Let A and C complete the work in x days
(A + B)s 1 days work =$$\frac{1}{8}$$
(B + C)s 1 days work =$$\frac{1}{12}$$and (C + A)s 1 days work =$$\frac{1}{x}$$
Then (A + B + B + C + C + A)s 1 day s work =$$\frac{1}{8}$$+$$\frac{1}{12}$$+$$\frac{1}{x}$$
2(A + B + C)s 1 days work =$$\frac{5x+24}{24x*2}$$
According to the question,
(A + B + C)s 1 days work =$$\frac{1}{6}$$=$$\frac{5x+24}{48x}$$
30x + 144 = 48x
x =$$\frac{144}{18}$$= 8 days.

Ans .

(1)24 days

1. Explanation :

As 1 days work = $$\frac{1}{12}$$
(A+B)s 1 days work = $$\frac{1}{8}$$
Bs 1 days work=$$\frac{1}{8}$$ -$$\frac{1}{12}$$ =$$\frac{3-2}{24}$$ = $$\frac{1}{24}$$
B alone can do the work in 24 days.

Ans .

(2)24 days

1. Explanation :

(2) (A + B)s 1 days work =$$\frac{1}{18}$$
(B + C)s 1 days work =$$\frac{1}{9}$$ and (A + C)s 1 days work =$$\frac{1}{12}$$
2 (A + B + C)s 1 days work =$$\frac{1}{18}$$ +$$\frac{1}{9}$$ +$$\frac{1}{12}$$ =$$\frac{2+4+3}{36}$$ =$$\frac{9}{36}$$ =$$\frac{1}{4}$$
(A + B + C)s 1 days work =$$\frac{1}{8}$$
B1s 1 days work = (A + B + C)s 1 days work - (A + C)s 1 days work =$$\frac{1}{8}$$ -$$\frac{1}{12}$$=$$\frac{3-2}{24}$$=$$\frac{1}{24}$$
Hence, B alone can do the work in 24 days.

Ans .

(1)3 days

1. Explanation :

(1) A alone can complete the work in 42 days working 1 hour daily. Similarly, B will take 56 days working 1 hour daily.
As 1 days work = $$\frac{1}{42}$$
Bs 1 day’s work = $$\frac{1}{56}$$
(A + B)s 1 days work =$$\frac{1}{42}$$ +$$\frac{1}{56}$$ =$$\frac{4+3}{168}$$ =$$\frac{7}{168}$$
= Time taken by (A + B) working 8 hours daily = $$\frac{168} {7}$$= 3 days.

Ans .

(3)40 days

1. Explanation :

(3) (A + B)s 1 days work =$$\frac{1}{10}$$.............. (i)
(B + C)s 1 days work=$$\frac{1}{12}$$............. (ii) and (C + A)s 1 days work = $$\frac{1}{15}$$............... (iii)
On adding all these, 2(A + B + C)s 1 days work=$$\frac{1}{10}$$+$$\frac{1}{12}$$+$$\frac{1}{15}$$ =$$\frac{6+5+4}{60}$$ =$$\frac{1}{4}$$
(A + B + C)s 1 day work=$$\frac{1}{8}$$................ (iv)
Cs 1 days work =$$\frac{1}{8}$$ -$$\frac{1}{10}$$=$$\frac{5-4}{40}$$=$$\frac{1}{40}$$
C will finish the work in 40 days.

Ans .

(1)60 days

1. Explanation :

(1) (A + B)s 1 days work =$$\frac{1}{15}$$
Bs 1 days work =$$\frac{1}{20}$$
As 1 days work =$$\frac{1}{15}$$ - $$\frac{1}{20}$$ =$$\frac{4-3}{60}$$ =$$\frac{1}{60}$$
A alone will do the work in 60 days.

Ans .

(4)20 days

1. Explanation :

(4) (A + B)s 1 days work =$$\frac{1}{12}$$ ,/br> (B + C)s 1 days work =$$\frac{1}{15}$$ and (C + A)s 1 days work =$$\frac{1}{20}$$
On adding, 2 (A + B + C)s 1 days work =$$\frac{1}{12}$$ +$$\frac{1}{15}$$+$$\frac{1}{20}$$ =$$\frac{5+4+3}{60}$$ =$$\frac{1}{5}$$
(A+B+C)s 1 days work =$$\frac{1}{10}$$
Bs 1 days work =$$\frac{1}{10}$$ - $$\frac{1}{20}$$ $$\frac{2-1}{20}$$ $$\frac{1}{20}$$
B alone can do the work in 20 days.

Ans .

(3)30 days

1. Explanation :

(3) (P + Q)s 1 days work=$$\frac{1}{12}$$...(i)
(Q + R)s 1 days work =$$\frac{1}{15}$$..(ii) and (R + P)s 1 days work =$$\frac{1}{20}$$ ...(iii)
Adding all three equations, 2 (P + Q + R)s 1 days work= $$\frac{1}{12}$$ +$$\frac{1}{15}$$+$$\frac{1}{20}$$ =$$\frac{5+4+3}{60}$$=$$\frac{12}{60}$$=$$\frac{1}{5}$$
(P + Q + R)s 1 days work=$$\frac{1}{10}$$
Ps 1 days work=$$\frac{1}{10}$$-$$\frac{1}{15}$$=$$\frac{3-2}{30}$$$$\frac{1}{30}$$
P alone will complete the work in 30 days.

Ans .

(3)6 days

1. Explanation :

(A + B)s 1 days work =$$\frac{1}{8}$$
(B + C)s 1 days work =$$\frac{1}{12}$$ and (C + A)s 1 days work =$$\frac{1}{8}$$
On adding, 2 (A + B + C)s 1 days work =$$\frac{1}{8}$$+$$\frac{1}{12}$$+$$\frac{1}{8}$$=$$\frac{3+2+3}{24}$$=$$\frac{8}{24}$$=$$\frac{1}{3}$$
(A + B + C)s 1 days work =$$\frac{1}{6}$$ Hence, the work will be completed in 6 days.

Ans .

(3)5$$\frac{5}{7}$$ days

1. Explanation :

(3) (A + B)s 1 days work =$$\frac{1}{10}$$
(B + C)s 1 days work = $$\frac{1}{6}$$ and (C + A)s 1 days work = $$\frac{1}{12}$$
Adding all three 2 (A + B + C)s 1 days work = $$\frac{1}{10}$$+$$\frac{1}{6}$$+$$\frac{1}{12}$$=$$\frac{6+10+5}{60}$$=$$\frac{21}{60}$$=$$\frac{7}{20}$$
(A + B + C)s 1 days work = $$\frac{7}{40}$$
All three together will complete the work in= $$\frac{40}{7}$$ = 5$$\frac{5}{7}$$days.

Ans .

(2) 2 hours

1. Explanation :

(2) (A + B)s 1 hours work =$$\frac{2}{9}$$ .....(i)
(B + C)s 1 hours work =$$\frac{1}{3}$$ .....(ii) and (C + A)s 1 hours work =$$\frac{4}{9}$$...(iii)
Adding all three equations, 2 (A + B + C)s 1 hours work= $$\frac{2}{9}$$+$$\frac{1}{3}$$+$$\frac{4}{9}$$=$$\frac{2+3+4}{9}$$=1
A, B and C together will complete the work in 2 hours.

Ans .

(1)16 days

1. Explanation :

(1) (A + B)s 1 days work =$$\frac{1}{18}$$
(B + C)s 1 days work = $$\frac{1}{24}$$ and (A + C)s 1 days work =$$\frac{1}{36}$$
Adding all three, 2 (A + B + C)s 1 days work= $$\frac{1}{18}$$+$$\frac{1}{24}$$+$$\frac{1}{36}$$=$$\frac{4+3+2}{71}$$=$$\frac{1}{8}$$
(A + B + C) 1 days work =$$\frac{1}{16}$$
A, B and C together will complete the work in 16 days.

Ans .

(3)13$$\frac{1}{3}$$days

1. Explanation :

(3) (A + B)s 1 days work =$$\frac{1}{5}$$ and As 1 days work = $$\frac{1}{8}$$
Bs 1 days work =$$\frac{1}{5}$$-$$\frac{1}{8}$$=$$\frac{8-5}{40}$$
B alone will complete the work in $$\frac{40}{3}$$=13$$\frac{1}{3}$$ days.

Ans .

(2)75 minutes

1. Explanation :

(2) Work done by (A + B + C) in 1 minute =$$\frac{1}{30}$$
Work done by (A + B) in 1 minute =$$\frac{1}{50}$$
Work done by C alone in 1 minute =$$\frac{1}{30}$$-$$\frac{1}{50}$$=$$\frac{5-3}{150}$$=$$\frac{2}{150}$$=$$\frac{1}{75}$$.
C alone will complete the work in 75 minutes.

Ans .

(1) 60 day

1. Explanation :

(1) (A + B)’s 1 day’s work =$$\frac{1}{8}$$
(B + C)s 1 days work =$$\frac{1}{24}$$ and (C + A)s 1 days work =$$\frac{7}{60}$$
On adding all three, 2 (A + B + C)’s 1 day’s work=$$\frac{1}{8}$$+$$\frac{1}{24}$$+$$\frac{7}{60}$$=$$\frac{15+5+14}{120}$$=$$\frac{34}{120}$$,/br> (A + B + C)s 1 day’s work =$$\frac{17}{120}$$
C’s 1 day’s work =$$\frac{17}{120}$$-$$\frac{1}{8}$$=$$\frac{17-15}{120}$$=$$\frac{1}{60}$$

br> C alone will complete the work in 60 days

Ans .

(1) 24 days

1. Explanation :

(1) (A+B)s 1 days work =$$\frac{1}{10}$$ and (B + C)s 1 days work =$$\frac{1}{12}$$
(C + A)s 1 days work = $$\frac{1}{15}$$
On adding all three, 2(A + B + C)s 1 days work=$$\frac{1}{10}$$+$$\frac{1}{12}$$+$$\frac{1}{15}$$=$$\frac{6+5+4}{60}$$=$$\frac{15}{60}$$=$$\frac{1}{4}$$
(A + B + C)s 1 days work = $$\frac{1}{8}$$
As 1 days work = $$\frac{1}{8}$$-$$\frac{1}{12}$$=$$\frac{3-2}{24}$$=$$\frac{1}{24}$$
A will complete the work in 24 days.

Ans .

(3)8$$\frac{4}{7}$$ days

1. Explanation :

(3) (A + B)s 1 days work =$$\frac{1}{20}$$
(B + C)s 1 days work =$$\frac{1}{10}$$ and (C + A)s 1 days work =$$\frac{1}{12}$$
On adding all three, 2 (A + B + C)’s 1 days work=$$\frac{1}{20}$$+$$\frac{1}{10}$$+$$\frac{1}{12}$$=$$\frac{3+6+5}{60}$$=$$\frac{14}{60}$$=$$\frac{7} {30}$$
(A + B + C)s 1 days work =$$\frac{7}{60}$$
Hence, the work will be completed in $$\frac{60}{7}$$= 8$$\frac{4}{7}$$days.

Ans .

(3)4 days

1. Explanation :

(3) Work done by A, B and C in 1 day=$$\frac{1}{10}$$ +$$\frac{1}{12}$$ +$$\frac{1}{15}$$ =$$\frac {6+5+4}{60}$$ =$$\frac{15}{60}$$ =$$\frac{1}{4}$$
Required time = 4 days

Ans .

(1) 20 days

1. Explanation :

(1) As 1 days work =$$\frac{1}{12}$$ -$$\frac{1}{30}$$ =$$\frac{5-2}{60}$$ =$$\frac{3}{60}$$ = $$\frac{1}{20}$$
Hence, A alone will complete the work in 20 days.

Ans .

(3)6$$\frac{6}{11}$$days

1. Explanation :

(3) (A + B + C)s 1 days work =$$\frac{1}{12}$$+$$\frac{1}{24}$$+$$\frac{1}{36}$$=$$\frac{6+3+2}{72}$$=$$\frac{11}{72}$$
(A + B + C) together will complete the work in$$\frac{72}{11}$$days=6$$\frac{6}{11}$$days

Ans .

(4)4 days

1. Explanation :

(4) (A + B)s 1 days work =$$\frac{1}{6}$$+$$\frac{1}{12}$$=$$\frac{2+1}{12}$$=$$\frac{1}{4}$$
A and B together will complete the work in 4 days.

Ans .

(3) 120 days

1. Explanation :

(2) (A + B)s 1 days work =$$\frac{1}{36}$$
(B + C)s 1 days work =$$\frac{1}{60}$$ and (C + A)s 1 days work =$$\frac{1}{45}$$
1 45 Adding all three, 2(A + B + C)s 1 days work=$$\frac{1}{36}$$+$$\frac{1}{60}$$+$$\frac{1}{45}$$=$$\frac{5+3+4}{180}$$=$$\frac{1}{15}$$
(A + B + C)s 1 days work =$$\frac{1}{30}$$
Cs 1 days work =$$\frac{1}{30}$$-$$\frac{1}{36}$$=$$\frac{6-5}{180}$$=$$\frac{1}{180}$$
Hence, C alone will finish the work in 180 days

Ans .

(3) 8 hrs. 15 min

1. Explanation :

(3) Ronald’s 1 hour’s work=$$\frac{32}{6}$$=$$\frac{16}{3}$$pages
[Pages typed in 6 hrs. = 32 pages typed in 1 hr =$$\frac{32}{6}$$]
Elans 1 hours work = 8 pages 1 hours work of the both=$$\frac{16}{3}$$+8=$$\frac{40}{3}$$pages.
Required time=$$\frac{110*3}{40}$$=$$\frac{33}{4}$$hours
=8 hours 15 minutes

Ans .

(4)12 days

1. Explanation :

(4) As 1days work =$$\frac{1}{20}$$
Bs 1days work =$$\frac{1}{30}$$
(A + B)s 1 days work =$$\frac{1}{20}$$+$$\frac{1}{30}$$=$$\frac{3+2}{60}$$=$$\frac{1}{12}$$
Hence, the work will be completed in 12 days. When worked together.

Ans .

(2) 24 hrs

1. Explanation :

(2) 9 hours 36 minutes=9+$$\frac{36}{60}$$ =9$$\frac{3}{5}$$hours=
=$$\frac{48}{5}$$
(A + B)s 1 hours work =$$\frac{5}{48}$$ and Cs 1 hours work =$$\frac{1}{48}$$
(A + B + C)s 1 hours work = $$\frac{5}{48}$$+$$\frac{1}{48}$$=$$\frac{1}{8}$$....(i)
As 1 hours work = (B + C)’s 1 hours work .....(ii)
From equations (i) and (ii), 2 × (As 1 hours work) = $$\frac{1}{8}$$
As 1 hours work = $$\frac{1}{16}$$
Bs 1 hours work =$$\frac{5}{48}$$-$$\frac{1}{16}$$=$$\frac{5-3}{48}$$=$$\frac{1}{24}$$
B alone will finish the work in 24 hours .

Ans .

(1)3

1. Explanation :

(1) Work done by A and B in 5 days =5($$\frac{1}{12}$$+$$\frac{1}{15}$$)=5($$\frac{5+4}{60}$$)
=5*$$\frac{9}{60}$$=$$\frac{9}{12}$$=$$\frac{3}{4}$$
Remaining work = 1-$$\frac{3}{4}$$=$$\frac{1}{4}$$
Time taken by A = $$\frac{1}{4}$$*12 = 3 days.

Ans .

(4)21 days

1. Explanation :

(2) Bs 1 days work = (A + B)s 1 days work - As 1 days work=$$\frac{1}{12}$$-$$\frac{1}{28}$$= $$\frac{7-3}{84}$$=$$\frac{4}{84}$$=$$\frac{1}{21}$$. Required time = 21 days.

Ans .

(4) ($$\frac{mn}{m+n}$$) days

1. Explanation :

4) As 1 days work =$$\frac{1}{m}$$and Bs 1 days work =$$\frac{1}{n}$$
(A + B)s 1 days work =$$\frac{1}{m}$$+$$\frac{1}{n}$$=$$\frac{n+m}{m}$$=$$\frac{m+n}{mn}$$
Required time = ($$\frac{mn}{m+n}$$) days

Ans .

(4) $$\frac{4}{3}$$hour

1. Explanation :

(4) Let A, B and C together do the work in x hours.
Time taken by A = (x + 6) hours Time taken by B= (x + 1) hours Time taken by C = 2x hours
=>$$\frac{1}{x+6}$$+$$\frac{1}{x+1}$$+$$\frac{1}{2x}$$=$$\frac{1}{x}$$
=>$$\frac{1}{x+6}$$+$$\frac{1}{x+1}$$=$$\frac{1}{x}$$-$$\frac{1}{2x}$$=$$\frac{1}{2x}$$
=>$$\frac{1}{x+6}$$=$$\frac{1}{2x}$$-$$\frac{1}{x+1}$$=$$\frac{x+1-2x}{2x(x+1)}$$
=>$$\frac{1}{x+6}$$=1-x/ 2x2+2x
=>2x 2+ 2x = x + 6 – x2 – 6x
=>3x 2 + 7x – 6 = 0
=> 3x 2 + 9x – 2x – 6 = 0
=> 3x (x + 3) – 2 (x + 3) = 0
=>(3x – 2) (x +3) = 0
=>3x – 2 = 0 as x + 3 != 0
=> x= $$\frac{2}{3}$$
Time taken by A =6+$$\frac{2}{3}$$=$$\frac{18+2}{3}$$=$$\frac{20}{3}$$hours
Time taken by B =1+$$\frac{2}{3}$$=$$\frac{5}{3}$$hours
(A +B)’s 1 hour’s work=$$\frac{3}{20}$$+$$\frac{5}{3}$$=$$\frac{3+12}{20}$$=$$\frac{15}{20}$$=$$\frac{3}{4}$$
Required time =$$\frac{4}{3}$$hour.

Ans .

(2) 96

1. Explanation :

(2) Time taken by B and C = x days (let)
Time taken by A = 3x days
Part of work done by A, B and C in 1 day= $$\frac{1}{x}$$ +$$\frac{1}{3x}$$=$$\frac{3+1}{3x}$$=$$\frac{4}{3x}$$
=> $$\frac{4}{3x}$$=$$\frac{1}{24}$$ => 3x = 4 × 24
=> x= $$\frac{4*24}{3}$$=32days
Time taken by A = 32 × 3 = 96 days

Ans .

(4) 3 days

1. Explanation :

(3) (4) As 1 days work =$$\frac{1}{4}$$
Bs 1 days work = $$\frac{1}{12}$$
(A + B)s 1 days work =$$\frac{1}{4}$$ +$$\frac{1}{12}$$ =$$\frac{3+1}{12}$$ =$$\frac{4}{12}$$ =$$\frac{1}{3}$$
Required time = 3 days.

Ans .

(3) 24 days

1. Explanation :

(3) A does $$\frac{1}{4}$$ work in 10 days
A will do 1 work in 10 × 4 = 40 days
Similarly, B will do the same work in 20 × 3 = 60 days
(A + B)s 1 days work =$$\frac{1}{40}$$+$$\frac{1}{60}$$ = $$\frac{3+2}{120}$$=$$\frac{5}{120}$$ = $$\frac{1}{24}$$
Required time = 24 days .

Ans .

(2)10 hours

1. Explanation :

(2) Using Rule 1, M1 D1 T1 = M2D2T2
=>15 × 20 × 8 = 20 × 12 × T2
=> T2 = $$\frac{15*20*8}{20*12}$$ =10 hours.

Ans .

(4) 60 days

1. Explanation :

4) (Raj + Ram)s 1 days work =$$\frac{1}{10}$$
Rajs 1 days work = $$\frac{1}{12}$$
Rams 1 day’s work = $$\frac{1}{10}$$-$$\frac{1}{12}$$ = $$\frac{6-5}{60}$$ = $$\frac{1}{60}$$
Required time = 60 days

Ans .

(2) 11 days

1. Explanation :

(2) As 1 days work =$$\frac{1}{9}$$
Bs 1 days work = $$\frac{1}{15}$$
Work done in first 2 days = As 1 days work + Bs 1 days work = $$\frac{1}{9}$$+$$\frac{1}{15}$$= $$\frac{5+3}{45}$$ = $$\frac{8}{45}$$
Work done in first 10 days = $$\frac{8*5}{45}$$ =$$\frac{8}{9}$$
Remaining work = 1-$$\frac{8}{9}$$ =$$\frac{1}{9}$$
Now, it is turn of 'A' for the eleventh day.
Time taken by 'A' in doing $$\frac{1}{9}$$ work = $$\frac{1}{9}$$ *9 = 1 day
Required time = 10 + 1 = 11 days.

Ans .

(4) 63

1. Explanation :

(4) Using Rule 1,
15 men complete $$\frac{1}{3}$$work in 7 days.
Time taken in doing 1 work = 3 × 7 = 21 days
=> M1D = M2D2
=>15 × 21 = M2 × 5
=>M2= $$\frac{15*21}{5}$$ = 63 days.s

Ans .

(2) 160 minutes

1. Explanation :

(2) (x and y)s 1 hour work = $$\frac{1}{4}$$ +$$\frac{1}{8}$$ = $$\frac{2+1}{8}$$ = $$\frac{3}{8}$$
Required time =$$\frac{8}{3}$$ hours
= ($$\frac{8}{3}$$*60) minutes. => 160 minutes.

Ans .

(1) 20 hours

1. Explanation :

(1) Number of pages copied by x in hour =$$\frac{80}{20}$$=4
Number of pages copied by x and y in 1 hour =$$\frac{135}{27}$$= 5
Number of pages copied by y in 1 hour = 5 – 4 = 1
Required time = 20 hours.

Ans .

(2)24

1. Explanation :

(2) (A + B)s 1 days work = $$\frac{1}{15}$$....(i)
(B + C)s 1 days work = $$\frac{1}{12}$$ .... (ii) and (C + A)s 1 days work = $$\frac{1}{10}$$.... (iii)
On adding all three equations, 2 (A + B + C)’s 1 days work = $$\frac{1}{15}$$+$$\frac{1}{12}$$+$$\frac{1}{10}$$
=$$\frac{4+6+5}{60}$$ =$$\frac{15}{60}$$ = $$\frac{1}{4}$$
(A + B + C)s 1 days work = $$\frac{1}{8}$$....(iv)
By equation (iv) – (ii), As 1 days work = $$\frac{1}{8}$$- $$\frac{1}{12}$$ = $$\frac{3-2}{24}$$ = $$\frac{1}{24}$$
Required time = 24 days.

Ans .

(3)$$\frac{19}{30}$$

1. Explanation :

(3)(A + B)s 1 days work =$$\frac{1}{25}$$+$$\frac{1}{30}$$ = $$\frac{6+5}{150}$$=$$\frac{11}{150}$$
(A + B)s 5 days work =$$\frac{5*11}{150}$$=$$\frac{11}{30}$$
Remaining work =1-$$\frac{11}{30}$$=$$\frac{30-11}{30}$$ =$$\frac{19}{30}$$

Ans .

(3) 9

1. Explanation :

(3)(A + B)s 1 days work = $$\frac{1}{6}$$ As 1 days work =$$\frac{1}{18}$$
Bs 1 days work =$$\frac{1}{6}$$-$$\frac{1}{18}$$= $$\frac{3-1}{18}$$ = $$\frac{2}{18}$$ = $$\frac{1}{9}$$
Required time = 9 days

Ans .

(2) 12 days

1. Explanation :

(2) As 2 days work = Bs 3 days work
Time taken by A = 8 days
Time taken by B =$$\frac{8}{2}$$ *3 =>12 days.

Ans .

(3) 8 days

1. Explanation :

Ans .

(2) 8 days

1. Explanation :

(2)(A + B)s 1 days work =$$\frac{1}{8}$$
(B + C)s 1 days work =$$\frac{1}{12}$$ and (A + B + C)s 1 days work =$$\frac{1}{6}$$ Cs 1 days work = $$\frac{1}{6}$$-$$\frac{1}{8}$$=$$\frac{4-3}{24}$$=$$\frac{1}{24}$$
As 1 days work =$$\frac{1}{6}$$-$$\frac{1}{12}$$= $$\frac{2-1}{12}$$= $$\frac{1}{12}$$
(A + C)s 1 days work =$$\frac{1}{12}$$+$$\frac{1}{24}$$=$$\frac{2+1}{24}$$=$$\frac{1}{8}$$
Required time = 8 days

Ans .

(3)$$\frac{7}{9}$$

1. Explanation :

(3)Using Rule 1,
(M1D1T1) / (W1) = (M2D2T2) / (W2)
= $$\frac{90*16*12}{1}$$ = (70*24*8 ) / (W2)
W2 = $$\frac{90*16*12}{70*24*8 }$$ = $$\frac{7}{9}$$ parts

Ans .

(3)12 days

1. Explanation :

(3) Let the work be completed in x days.
According to the question,
$$\frac{x}{16}$$+$$\frac{x-8}{32}$$+$$\frac{x-6}{48}$$ =1
$$\frac{6x+3x-24+2x-12 }{96}$$ =1
11x – 36 = 96
11x = 96 + 36 = 132
x =$$\frac{132}{11}$$ =12 days.

Ans .

(3) 8 days

1. Explanation :

(3) (A+B)s 1 days work =$$\frac{1}{15}$$
(B+C)s 1 days work =$$\frac{1}{10}$$ and (A+C)s 1 days work =$$\frac{1}{12}$$ On adding all three, 2(A+B+C)s 1 days work =$$\frac{1}{15}$$+$$\frac{1}{10}$$+$$\frac{1}{12}$$ =$$\frac{4+6+5}{60}$$ =$$\frac{15}{60}$$=$$\frac{1}{4}$$
(A + B + C)s 1 days work =$$\frac{1}{8}$$
Required time = 8 days.

Ans .

(3 7

1. Explanation :

(3) Let the whole work be completed in x days
As 1 days work =$$\frac{1}{10}$$
Bs 1 days work =$$\frac{1}{12}$$ and Cs 1 days work =$$\frac{1}{15}$$
According to the question, As (x – 5) days work + Bs (x – 3) days work + Cs x days work = 1
=>$$\frac{x-5}{10}$$ +$$\frac{x-3}{12}$$ +$$\frac{x}{15}$$ = 1
=> $$\frac{x-5}{10}$$+$$\frac{x-3}{12}$$+$$\frac{x}{15}$$ = 1
=> $$\frac{6(x-5)+5(x-3)+4x}{60}$$ =1
=> 6x – 30 + 5x – 15 + 4x = 60
=>15x – 45 = 60
=> 15x = 60 + 45 = 105
=> x=$$\frac{105}{15}$$ = 7 days.

Ans .

(2)3$$\frac{1}{13}$$days

1. Explanation :

As 1 days work =$$\frac{1}{24}$$
Bs 1 days work =$$\frac{1}{5}$$ and C 1 days work =$$\frac{1}{12}$$
(A + B + C)s 1 days work = $$\frac{1}{24}$$ +$$\frac{1}{5}$$ +$$\frac{1}{12}$$ =$$\frac{5+24+10}{120}$$ =$$\frac{39}{120}$$ =$$\frac{13}{40}$$
Required Time=$$\frac{40}{13}$$ =3$$\frac{1}{13}$$ days.

Ans .

(4)10 days

1. Explanation :

Ans .

(1)5$$\frac{1}{7}$$days

1. Explanation :

(1) As 1 days work =$$\frac{1}{9}$$
Bs 1 days work = 5$$\frac{1}{12}$$
(A + B)s 1 day’s work = $$\frac{1}{9}$$+$$\frac{1}{12}$$= $$\frac{4+3}{36}$$ = $$\frac{7}{36}$$
Required time = $$\frac{36}{7}$$ =5$$\frac{1}{7}$$days.

Ans .

(1) 60 hours

1. Explanation :

(1) Let time taken by son be x hours.
Father’s and sons 1 days work = $$\frac{1}{30}$$+$$\frac{1}{x}$$
$$\frac{1}{30}$$+$$\frac{1}{x}$$ =$$\frac{1}{20}$$
=>$$\frac{1}{x}$$= $$\frac{1}{20}$$-$$\frac{1}{30}$$
=$$\frac{3-2}{60}$$=$$\frac{1}{60}$$
=> x = 60 hour.

Ans .

(2)9days

1. Explanation :

(2) Work done by (A + B) in 5 days = 5($$\frac{1}{12}$$+$$\frac{1}{20}$$ )
=5($$\frac{5+3}{60}$$ ) = $$\frac{40}{60}$$ =$$\frac{2}{3}$$
Remaining work = 1-$$\frac{2}{3}$$ =$$\frac{1}{3}$$
Time taken by C in doing $$\frac{1}{3}$$ work = 3 days
Required time = 3 × 3 = 9 days.

Ans .

(3)3$$\frac{15}{16}$$

1. Explanation :

(3) As 1 days work =$$\frac{1}{7}$$
Bs 1 days work =$$\frac{1}{9}$$
(A + B)s 1 days work =$$\frac{1}{7}$$+$$\frac{1}{9}$$ =$$\frac{9+7}{63}$$ =$$\frac{16}{63}$$
\ Required time =$$\frac{63}{16}$$ days =3$$\frac{15}{16}$$days.

Ans .

(1) 12 days

1. Explanation :

(1) (A + B)s 1 days work =$$\frac{1}{24}$$
(A + B + C)s 1 days work =$$\frac{1}{8}$$
Cs 1 days work = $$\frac{1}{24}$$ -$$\frac{1}{8}$$ =$$\frac{3-1}{24}$$ =$$\frac{2}{24}$$ =$$\frac{1}{12}$$
Required time = 12 days.

Ans .

(4) 8 days

1. Explanation :

(4) (A + B)’s 1 day’s work=$$\frac{1}{12}$$+$$\frac{1}{24}$$=$$\frac{2+1}{24}$$=$$\frac{3}{24}$$=$$\frac{1}{8}$$
Required time = 8 days.

Ans .

(4)8

1. Explanation :

(4) (A + B)s 1 days work =$$\frac{1}{11}$$+$$\frac{1}{20}$$ =$$\frac{20+11}{220}$$=$$\frac{31}{220}$$
(A + C)’s 1 days work =$$\frac{1}{11}$$+$$\frac{1}{55}$$=$$\frac{5+1}{55}$$=$$\frac{6}{55}$$
Work done in first two days = $$\frac{31}{220}$$+$$\frac{6}{55}$$ =$$\frac{31+24}{220}$$=$$\frac{55}{220}$$=$$\frac{1}{4}$$
Required time = 2 × 4 = 8 days.

Ans .

(1)18 days

1. Explanation :

(1) (A + B)s 1 days work =$$\frac{1}{6}$$
As 1 days work =$$\frac{1}{9}$$
B’s 1 day’s work =$$\frac{1}{6}$$-$$\frac{1}{9}$$=$$\frac{3-2}{18}$$=$$\frac{1}{18}$$
Required time = 18 days.

Ans .

(2) 24 days

1. Explanation :

As 1 days work =$$\frac{1}{18}$$
As 12 days work =$$\frac{12}{18}$$=$$\frac{2}{3}$$
=>Remaining work =1-$$\frac{2}{3}$$ =$$\frac{1}{3}$$
Time taken by B in doing $$\frac{1}{3}$$ work = 8 days
Time taken by B in doing whole work = 3 × 8 = 24 days .

Ans .

(3)8 days

1. Explanation :

(3) (A + B)s 1 days work=$$\frac{1}{8}$$ ... (i)
(B + C)s 1 days work= $$\frac{1}{12}$$.... (ii) and (A + B + C)s 1 days work =$$\frac{1}{6}$$... (iii)
By equations (i) + (ii) – (iii), Bs 1 days work =$$\frac{1}{8}$$+$$\frac{1}{12}$$-$$\frac{1}{6}$$ = $$\frac{3+2-4}{24}$$ = $$\frac{1}{24}$$ .... (iv)
By equations (iii) – (iv), (A + C)’s 1 days work =$$\frac{1}{6}$$-$$\frac{1}{24}$$ = $$\frac{4-1}{24}$$= $$\frac{3}{24}$$ =$$\frac{1}{8}$$
Required time = 8 days

Ans .

(4)12 days

1. Explanation :

(4) Let time taken by A be x days.
Time taken by B = 3x days According to the question,
$$\frac{1}{x}$$+$$\frac{1}{3x}$$=$$\frac{1}{9}$$
=>$$\frac{3+1}{3x}$$ =$$\frac{1}{9}$$
=>3x = 4 × 9
=> x = $$\frac{4*9}{3}$$ =12 days.

Ans .

(4) 100 days

1. Explanation :

Ans .

(3)($$\frac{pq}{p+q}$$

1. Explanation :

(3) Xs 1 days work =$$\frac{1}{p}$$
Ys 1 day’s work =$$\frac{1}{q}$$
(X + Y)s 1 days work= $$\frac{1}{p}$$+$$\frac{1}{q}$$=$$\frac{q+p}{pq}$$
Required time =($$\frac{pq}{p+q}$$.

Ans .

(2)$$\frac{40}{9}$$

1. Explanation :

(2) As 1 days work =$$\frac{1}{8}$$ Bs 1 days work =$$\frac{1}{10}$$
(A + B)s 1 days work = $$\frac{1}{8}$$+$$\frac{1}{10}$$ =$$\frac{5+4}{40}$$=$$\frac{9}{40}$$
Required time = $$\frac{40}{9}$$ days

Ans .

(2) 16 days

1. Explanation :

(2) (A + B)s 1 days work =$$\frac{1}{36}$$
(B + C)s 1 days work = $$\frac{1}{24}$$ and (A + C)s 1 days work =$$\frac{1}{18}$$
On adding all three, 2 (A + B + C)s 1 days work =$$\frac{1}{36}$$+$$\frac{1}{24}$$+$$\frac{1}{18}$$ = $$\frac{2+3+4}{72}$$ =$$\frac{9}{72}$$ =$$\frac{1} {8}$$
(A + B + C)’s 1 day’s work =$$\frac{1}{36}$$
Required time = 16 days .

Ans .

$$\frac{xy}{x+y}$$ days

1. Explanation :

(3) Koushiks 1 days work =$$\frac{1}{x}$$
Krishnus 1 days work =$$\frac{1}{y}$$
One days work of both =$$\frac{1}{x}$$+$$\frac{1}{y}$$ =$$\frac{x+y}{xy}$$
Required time =$$\frac{xy}{x+y}$$ days.

Ans .

(2)8

1. Explanation :

M1D1 = M2D2
=>24 × 12 = 36 × D2
= D2 =$$\frac{24*12}{36}$$ = 8 days.

Ans .

(1)18 days

1. Explanation :

(3) (A + B)s 1 days work =$$\frac{1}{18}$$
(B + C)s 1 days work =$$\frac{1}{24}$$ and (C + A)s 1 days work =$$\frac{1}{36}$$
On adding all three, 2 (A + B + C)s 1 day’s work =$$\frac{1}{18}$$+$$\frac{1}{24}$$+$$\frac{1}{36}$$=$$\frac{4+3+2}{72}$$=$$\frac{9}{72}$$=$$\frac{1}{8}$$
(A + B + C)’s 1 days work =$$\frac{1}{16}$$
Required time = 16 days .

Ans .

(1) 10$$\frac{5}{24}$$ days

1. Explanation :

(1) As 4 days work = Bs 5 days work
=> A : B = 4 : 5
Again, B : C = 6 : 7
=> A : B : C = 4 × 6 : 5 × 6 : 5 × 7 = 24 : 30 : 35
Q Time taken by A = 7 days
Time taken by C =$$\frac{35}{24}$$ * 7 =$$\frac{245}{24}$$ =10$$\frac{5}{24}$$ days.

Ans .

(2)7 days

1. Explanation :

Ans .

(2)2

1. Explanation :

(2) Work done by two sons in an hour =$$\frac{1}{3}$$+$$\frac{1}{6}$$=$$\frac{2+1}{6}$$=$$\frac{1}{2}$$
Work done by father in an hour =$$\frac{1}{2}$$
Required time = 2 hours

Ans .

(4) 4 days

1. Explanation :

As 1 days work =$$\frac{1}{10}$$
Bs 1 days work =$$\frac{1}{12}$$ and Cs 1 day’s work =$$\frac{1}{15}$$
(A + B + C)’s 1 days work = $$\frac{1}{10}$$ +$$\frac{1}{12}$$ +$$\frac{1}{15}$$ =$$\frac{6+5+4}{60}$$ =$$\frac{15}{60}$$ =$$\frac{1}{4}$$
Required time = 4 days.

Ans .

(1) 20 mats

1. Explanation :

=>5 × 5 × x = 10 × 10 × 5 => x =$$\frac{10*10*5}{5*5}$$ = 20 mats.

Ans .

(2)20 days

1. Explanation :

(2) (A + B)s 1 days work =$$\frac{1}{12}$$
As 1 days work =$$\frac{1}{30}$$
Bs 1 day’s work =$$\frac{1}{12}$$-$$\frac{1}{30}$$ =$$\frac{5-2}{60}$$ =$$\frac{1}{20}$$ Required time = 20 days

Ans .

(2)48

1. Explanation :

(2) (Ganesh + Ram + Sohan)s 1 days work =$$\frac{1}{16}$$
(Ganesh + Ram)s 1 days work = $$\frac{1}{24}$$
Sohans 1 days work = $$\frac{1}{16}$$ -$$\frac{1}{24}$$ =$$\frac{3-2}{48}$$ =$$\frac{1}{48}$$
Required time = 48 days.

Ans .

(1) 120 days

1. Explanation :

(1) (A + B)s 1 days work= $$\frac{1}{72}$$ ..... (i)
(B + C)s 1 days work = $$\frac{1}{120}$$.... (ii) and (C + A)’s 1 day’s work = $$\frac{1}{90}$$..... (iii)
On adding all three, 2 (A + B + C)s 1 days work =$$\frac{1}{72}$$+$$\frac{1}{120}$$+$$\frac{1}{90}$$
=$$\frac{5+3+4}{360}$$ =$$\frac{12}{360}$$=$$\frac{1}{30}$$
(A + B + C)s 1 days work= $$\frac{1}{60}$$..... (iv)
As 1 days work = Equation (iv) – (ii),
$$\frac{1}{60}$$-$$\frac{1}{120}$$=$$\frac{2-1}{120}$$=$$\frac{1}{120}$$
Required time = 120 days .

Ans .

(2)28

1. Explanation :

Ans .

(3)17$$\frac{1}{7}$$ days

1. Explanation :

(3) As 1 days work =$$\frac{1}{30}$$
Bs 1 days work =$$\frac{1}{40}$$
(A + B)’s 1 day’s work =$$\frac{1}{30}$$+$$\frac{1}{40}$$= $$\frac{4+3}{120}$$=$$\frac{7}{120}$$
Required time =$$\frac{120}{7}$$=17$$\frac{1}{7}$$.

# TYPE-II

Ans .

(2) 5$$\frac{1}{3}$$days

1. Explanation :

(2) A can finish the work in 18 days.
As one days work = $$\frac{1}{18}$$
Similarly, Bs one days work = $$\frac{1}{24}$$
(A + B)s 8 days work =( $$\frac{1}{18}$$+$$\frac{1}{24}$$) *8 =$$\frac{7}{72}$$ *8=$$\frac{7}{9}$$
Remaining work = 1-$$\frac{7}{9}$$=$$\frac{2}{9}$$
Time taken to finish the remaining work by B is $$\frac{2}{9}$$ *24 = $$\frac{16}{3}$$ =5$$\frac{1}{3}$$days.

Ans .

(4) 13 days

1. Explanation :

(4) (A+B)s 2 days work =2($$\frac{1}{12}$$ +$$\frac{1}{18}$$ ) =$$\frac{10}{36}$$
Remaining work = 1 - $$\frac{10}{36}$$ =$$\frac{26} {36}$$
Time taken by B to complete $$\frac{26}{36}$$ part of work
=>$$\frac{26}{36}$$ *18= 13 days.

Ans .

(3) 6 days

1. Explanation :

(3) A1s one days work = $$\frac{1}{6}$$
Bs one days work =$$\frac{1}{12}$$
(A + B)s one days work =$$\frac{1}{6}$$ +$$\frac{1}{12}$$ =$$\frac{2+1}{12}$$ =$$\frac{1}{4}$$
(A + B)s three days work =$$\frac{3}{4}$$
Remaining work = 1-$$\frac{3}{4}$$= $$\frac{1}{4}$$
Total required number of days = $$\frac{1}{4}$$*$$\frac{12}{1}$$ +3= 3 + 3 = 6 days.

Ans .

(1) 18 days

1. Explanation :

(1) (A + B)s days work =$$\frac{1}{30}$$
(B + C)s 1 days work =$$\frac{1}{24}$$ and (C + A)s 1 days work =$$\frac{1}{20}$$
2 (A + B + C)s 1 days work =$$\frac{1}{30}$$+$$\frac{1}{24}$$+$$\frac{1}{20}$$ =$$\frac{4+5+6}{120}$$=$$\frac{15}{120}$$=$$\frac{1}{8}$$
(A + B + C)s 1 days work =$$\frac{1}{16}$$
(A + B + C)s 10 days’ work =$$\frac{10}{16}$$=$$\frac{5}{8}$$
Remaining work = 1 -$$\frac{5}{8}$$ =$$\frac{3}{8}$$
This part of work is done by A alone.
Now As 1 day’s work =$$\frac{1}{16}$$ -$$\frac{1}{24}$$ =$$\frac{3-2}{48}$$ =$$\frac{1}{48}$$
The required no. of days =$$\frac{3}{8}$$* 3= 18 days.

Ans .

(2)60 days

1. Explanation :

2) (A+B)s 1 days work =$$\frac{1}{30}$$
(A + B)s 20 days work =$$\frac{20}{30}$$ =$$\frac{2}{3}$$
Remaining work =1-$$\frac{2}{3}$$=$$\frac{1}{3}$$
Now,$$\frac{1}{3}$$part of work is done by A in 20 days.
Whole work will be done by A alone in 20 × 3 = 60 days

Ans .

(3) 4

1. Explanation :

Ans .

(3) 10 days

1. Explanation :

(3) Work done by (B + C) in 3 days = 3* ($$\frac{1}{9}$$ +$$\frac{1}{12}$$)
= $$\frac{1}{3}$$+$$\frac{1}{4}$$=$$\frac{4+3}{12}$$=$$\frac{7}{12}$$
Remaining work = 1-$$\frac{7}{12}$$ =$$\frac{5}{12}$$
This part of work is done by A alone.
Now, $$\frac{1}{24}$$ part of work is done by A in 1 day.
=> $$\frac{5}{12}$$ part of work will be done by A in = 24 ´*$$\frac{5}{12}$$ = 10 days.

Ans .

(2) 24 days

1. Explanation :

(2) Originally, let there be x men Now, more men, less days (x + 6) : x : : 55 : 44
so,$$\frac{x+6}{x}$$=$$\frac{55}{44}$$ =$$\frac{5}{4}$$
or 5x = 4x + 24 or x = 24.

Ans .

(3) 12 days

1. Explanation :

(3) Work done by 2 (A + B) in one day =( \frac{1}{10} \)+( \frac{1}{15} \) =( \frac{3+2}{30} \)=( \frac{5}{30} \)=( \frac{1}{6} \)
Work done by (A + B) in oneday =( \frac{1}{12} \)
(A + B) can complete the work in 12 days

Ans .

(3)8 days

1. Explanation :

(3) Let A worked for x days.
According to question $$\frac{x}{28}$$+$$\frac{(x+17)}{35}$$ =1
=>$$\frac{5x+4(x+17)}{140}$$ =1
=>5x + 4x + 68 = 140
=>9x = 140 – 68 = 72
=> x = 8
A worked for 8 days

Ans .

(3)12 days

1. Explanation :

(3) Work done by (A + B) in 1 day =$$\frac{1}{15}$$+$$\frac{1}{10}$$=$$\frac{2+3}{30}$$=$$\frac{1}{6}$$
(A + B)s 2 days work =$$\frac{2}{6}$$ =$$\frac{1}{3}$$
Remaining work =1 -$$\frac{1}{3}$$ =$$\frac{2}{3}$$
This part is done by A alone.
one work is done by A in 15 days.
$$\frac{2}{3}$$ work is done in 15*$$\frac{2}{3}$$
= 10 days.
Total number of days = 10 + 2 = 12 days

Ans .

(4)10 days

1. Explanation :

(1) As 1 days work =$$\frac{1}{20}$$.
As 4 days work =$$\frac{4}{20}$$ =$$\frac{1}{5}$$
This part is completed by A and B together.
Now, (A + B)s 1 days work = $$\frac{1}{20}$$+$$\frac{1}{12}$$=$$\frac{3+5}{60}$$=$$\frac{8}{60}$$=$$\frac{2}{15}$$
Now,$$\frac{2}{15}$$work is done by (A +B) in 1 day.
$$\frac{4}{5}$$ work is done in .
=$$\frac{15}{2}$$*$$\frac{4}{5}$$ = 6 days
Hence, the work lasted for 4 + 6 = 10 days.

Ans .

(2)9 days

1. Explanation :

(2) (A + B)s 1 days work =($$\frac{1}{45}$$ +$$\frac{1}{40}$$ ) =$$\frac{8+9}{360}$$ =$$\frac{17}{360}$$
Work done by B in 23 days = $$\frac{1}{4}$$ * 23 =$$\frac{23}{40}$$
Remaining work = 1- $$\frac{23}{40}$$= $$\frac{17}{40}$$
Now,$$\frac{17}{40}$$work was done by (A + B) in 1 day
$$\frac{17}{40}$$ work was done by (A + B) in 1 * $$\frac{360}{17}$$ *$$\frac{17}{40}$$ = 9 days.
Hence, A left after 9 days.

Ans .

(1)72 days

1. Explanation :

Ans .

(3)16 days

1. Explanation :

(3) Time taken by A = $$\frac{8*12}{4}$$ = 24days.
Work done of by B = $$\frac{4}{12}$$=$$\frac{1}{3}$$
Remaining work =1-$$\frac{1}{3}$$ = $$\frac{2}{3}$$
A can complete a work in 24 days
A can complete $$\frac{2}{3}$$ part of work in 24* $$\frac{2}{3}$$ = 16 days.

Ans .

(1)14$$\frac{1}{3}$$ days

1. Explanation :

(1) As 1 days work = $$\frac{1}{12}$$
Bs 1 days work = $$\frac{1}{18}$$
Part of work done by A and B in first two days = $$\frac{1}{12}$$+ $$\frac{1}{18}$$= $$\frac{3+2}{36}$$= $$\frac{5}{36}$$
Part of work done by A and B in 14 days =$$\frac{35}{36}$$
[14 days to be taken randomly] Remaining work = 1-$$\frac{35}{36}$$ =$$\frac{1}{36}$$
Now A will work for 15th day. A will do the $$\frac{1}{36}$$ work in $$\frac{1}{36}$$*12 =$$\frac{1}{3}$$ day.
Total Work will be done in 14$$\frac{1}{3}$$ days.

Ans .

(3)7 days

1. Explanation :

(3) Let the work be completed in x days.
According to the question ,$$\frac{x-5}{10}$$+$$\frac{x-3}{12}$$+$$\frac{x}{15}$$=1
=>$$\frac{6x-30+5x-15+4x}{60}$$ =1
=>15x – 45 = 60 ,/br> => 15x = 105
=> x =$$\frac{105}{15}$$ = 7 days.

Ans .

(4)8 days

1. Explanation :

Ans .

(1)56$$\frac{2}{3}$$ days

1. Explanation :

Ans .

(4)9 days

1. Explanation :

(4) Let the work be finished in x days.
According to the question,
A worked for x days while B worked for (x – 3) days
$$\frac{x}{18}$$+$$\frac{x-3}{12}$$=1
=>$$\frac{2x+3x-9}{36}$$ = 1
=> 5x – 9 = 36
=> 5x = 45
=> x = $$\frac{45}{5}$$= 9
Hence, the work was completed in 9 days.

Ans .

(1)6 days

1. Explanation :

(1) Let A and B worked together for x days
According to the question,
Part of work done by A for (x + 10) days + part of work done by B for x days = 1
=> $$\frac{x+10}{20}$$ +$$\frac{x}{30}$$ = 1
=> $$\frac{3x+30+2x}{60}$$ = 1
=>5x + 30 = 60
=> 5x = 30
=> x= $$\frac{30}{5}$$ = 6 days.

Ans .

(2)8 days

1. Explanation :

(2) Let the work be completed in x days.
According to the question,
A worked for (x –3) days, while B worked for x days.
$$\frac{x-3}{9}$$ +$$\frac{x}{18}$$ = 1
=>$$\frac{2x-6+x}{18}$$ = 1 => 3x–6 = 18
=>3x = 18 + 6 = 24
=> x =$$\frac{24}{3}$$ = 8 days.

Ans .

(3)15 days

1. Explanation :

(3) (B + C)s 2 days work= 2($$\frac{1}{30}$$ + ($$\frac{1}{20}$$)
= 2($$\frac{2+3}{60}$$) = $$\frac{1}{6}$$ part
Remaining work = 1- $$\frac{1}{6}$$= $$\frac{5}{6}$$ part.
Time taken by A to complete this part of work $$\frac{5}{6}$$ *18 = 15 days.

Ans .

(3)6 days

1. Explanation :

(3) Part of work done by B in 10 days = 10*$$\frac{1}{15}$$ = $$\frac{2}{3}$$
Remaining work =1 - $$\frac{1}{2}$$ = $$\frac{1}{3}$$
Time taken by A = $$\frac{1}{3}$$*18 = 6 days.

Ans .

(3)10$$\frac{1}{4}$$days

1. Explanation :

(3) Part of work done by A and B in first two days $$\frac{1}{9}$$ +$$\frac{1}{12}$$ = $$\frac{4+3}{36}$$ = $$\frac{7}{36}$$
Part of work done in first 10 days = $$\frac{35}{36}$$
Remaining work= 1-$$\frac{35}{36}$$ = $$\frac{1}{36}$$
Now it is the turn of A.
Time taken by A =$$\frac{1}{36}$$*9 = $$\frac{1}{4}$$day
Total time = 10 +$$\frac{1}{4}$$ =10$$\frac{1}{4}$$days.

Ans .

(4)15 days

1. Explanation :

(4) Bs 1 days work =$$\frac{1}{12}$$-$$\frac{1}{20}$$= $$\frac{5-3}{60}$$ =$$\frac{1}{30}$$
Bs $$\frac{1}{2}$$days work = $$\frac{1}{60}$$
(A + B)s 1 days work = $$\frac{1}{20}$$ + $$\frac{1}{60}$$ = $$\frac{3+1}{60}$$= $$\frac{1}{15}$$
[ B works for half day daily]
Hence, the work will be completed in 15 days

Ans .

(3)6 days

1. Explanation :

. (3) Part of the work done by A and B in 4 days = 2*($$\frac{1}{12}$$+$$\frac{1}{15}$$) = 4$$\frac{5+4}{60}$$
= 4*$$\frac{9}{60}$$ =$$\frac{3}{5}$$
Remaining work = 1-$$\frac{3}{5}$$ =$$\frac{2}{5}$$
Time taken by B to complete the remaining work =$$\frac{2}{5}$$ *15 =6 days

Ans .

(1)13$$\frac{1}{3}$$ days

1. Explanation :

(1) Part of the work done by X in 8 days=$$\frac{8}{40}$$=$$\frac{1}{5}$$
Remaining work = 1-$$\frac{1}{5}$$=$$\frac{4}{5}$$
This part of work is done by Y in 16 days.
Time taken by Y in doing 1 work =$$\frac{16*5}{4}$$ = 20 days.
Work done by X and Y in 1 day = $$\frac{1}{40}$$+$$\frac{1}{20}$$=$$\frac{1+2}{40}$$=$$\frac{3}{40}$$
Hence, both together will complete the work in$$\frac{40}{3}$$ i.e13$$\frac{1}{3}$$ days

Ans .

(1)9$$\frac{3}{8}$$ days

1. Explanation :

(1) Work done in first two days =$$\frac{2}{30}$$+$$\frac{1}{10}$$+$$\frac{1}{20}$$=$$\frac{1}{15}$$+$$\frac{1}{20}$$+$$\frac{1}{10}$$
=$$\frac{4+3+6}{60}$$ = $$\frac{13}{60}$$
Work done in first 8 days =$$\frac{52}{60}$$ Remaining work = 1-$$\frac{52}{60}$$ = $$\frac{8}{60}$$ = $$\frac{2}{15}$$
(A + B)s 1 days work = $$\frac{1}{30}$$ +$$\frac{1}{20}$$=$$\frac{2+3}{60}$$=$$\frac{1}{12}$$
Remaining work =$$\frac{2}{15}$$ -$$\frac{1}{12}$$ =$$\frac{8-5}{60}$$=$$\frac{3}{60}$$=$$\frac{1}{20}$$
(A + C)s 1 days work =$$\frac{1}{30}$$+$$\frac{1}{10}$$=$$\frac{1+3}{30}$$=$$\frac{2}{15}$$
Time taken =$$\frac{1}{20}$$*$$\frac{15}{2}$$
=$$\frac{3}{8}$$ day.
Total time = 9 +$$\frac{3}{8}$$ =9$$\frac{3}{8}$$ days

Ans .

(1)5 days

1. Explanation :

(1) Work done by B in 9 days = $$\frac{9}{12}$$ =$$\frac{3}{4}$$part
Remaining work = 1- $$\frac{3}{4}$$= $$\frac{1}{4}$$which is done by A
Time taken by A =$$\frac{1}{4}$$*20 = 5days.

Ans .

(2) 7$$\frac{1}{3}$$ days

1. Explanation :

(2) Work done by A in 6 days =$$\frac{6}{8}$$=$$\frac{3}{4}$$part
Work destroyed by B in 2 days =$$\frac{2}{3}$$part
Remaining work after destruction = $$\frac{3}{4}$$- $$\frac{2}{3}$$= $$\frac{9-8}{12}$$=$$\frac{1}{12}$$
Now, time taken by A in doing $$\frac{11}{12}$$ part
$$\frac{11}{12}$$ * 8 = $$\frac{22}{3}$$ =7$$\frac{1}{3}$$days.

Ans .

(1)6 days

1. Explanation :

(1) Work done by B in 10 days =$$\frac{10}{15}$$=$$\frac{2}{3}$$
Remaining work = 1-$$\frac{2}{3}$$=$$\frac{1}{3}$$
Time taken by A to complete the work = $$\frac{1}{3}$$ *18 = 6 days.

Ans .

(1)48 days

1. Explanation :

Ans .

(3) 120 days

1. Explanation :

(3) (A + B + C)s 1 days work = $$\frac{1}{20}$$+$$\frac{1}{30}$$+$$\frac{1}{60}$$ = $$\frac{3+2+1}{60}$$ = $$\frac{1}{10}$$
As 2 days work =$$\frac{2}{20}$$=$$\frac{1}{10}$$
Work done in first three days= $$\frac{1}{10}$$+$$\frac{1}{10}$$=$$\frac{2}{10}$$=$$\frac{1}{5}$$
[As work for 2 days + (A + B + C) work on 3rd day]
Hence, the work will be finished in 15 days.

Ans .

(3)6 days

1. Explanation :

(3) (A + B)s 2 days work =$$\frac{2}{3}$$
Remaining Work =1 - $$\frac{2}{3}$$ = $$\frac{1}{3}$$
Time taken by A in destroying $$\frac{1}{3}$$work = 2 days
Time taken by A in completing the work = 6 days
Bs 1 days work = $$\frac{1}{3}$$-$$\frac{1}{6}$$ =$$\frac{2-1}{6}$$ =$$\frac{1}{6}$$
B alone will complete the work in 6 days.

Ans .

(3)24 days

1. Explanation :

(3) Work done by A and B in 7 days=$$\frac{7}{20}$$+$$\frac{7}{30}$$=$$\frac{21+14}{60}$$=$$\frac{35} {60}$$=$$\frac{7}{12}$$
So, Remaining work = 1-$$\frac{7}{12}$$ =$$\frac{5}{12}$$
Time taken by C= $$\frac{12}{5}$$*10 = 24 days.

Ans .

(3)6$$\frac{2}{3}$$days

1. Explanation :

Ans .

(4) 4

1. Explanation :

(4) Work done by A and B in first 6 days
= (A + B)s 4 days work + Bs 2 days work =4*$$\frac{1}{8}$$+$$\frac{1}{12}$$
=$$\frac{1}{2}$$+$$\frac{1}{6}$$= $$\frac{3+1}{6}$$ =$$\frac{2}{3}$$
Remaining work = 1-$$\frac{2}{3}$$ =$$\frac{1}{3}$$
Time taken by C =$$\frac{1}{3}$$*12 = 4days.

Ans .

(1)60 days

1. Explanation :

(1) (A + B) together do the work in 30 days
(A + B)s 1 days work =$$\frac{1}{30}$$
(A + B)s 20 days work =$$\frac{20}{30}$$ =$$\frac{2}{3}$$
Remaining work =1-$$\frac{2}{3}$$ = $$\frac{1}{3}$$
Time taken by A in doing $$\frac{1}{3}$$ work = 20 days
Time taken in doing 1 work= 20 × 3 = 60 days.

Ans .

(3) 3$$\frac{1}{2}$$days

1. Explanation :

(3) Remaining work =1-$$\frac{1}{8}$$ =$$\frac{7}{8}$$
(A + B)s 1 days work =$$\frac{1}{6}$$+$$\frac{1}{12}$$=$$\frac{2+1}{12}$$=$$\frac{3}{12}$$=$$\frac{1}{4}$$
Time taken in doing $$\frac{7}{8}$$part of work =$$\frac{7}{8}$$*4= $$\frac{7}{2}$$= 3$$\frac{1}{2}$$days

Ans .

(2)6

1. Explanation :

(2) Work done by 12 men in 8 days = Work done by 16 women in 12 days.
=> 12 × 8 men
=> 16 × 12 women
=>1 man => 2 women
Now, work done by 12 men in 1 day =$$\frac{1}{8}$$
1 mans 1 days work = $$\frac{1}{12*8}$$ =$$\frac{1}{96}$$
16 mens 3 days work

Ans .

(2)8

1. Explanation :

Ans .

(1) 44

1. Explanation :

12 men =24 boys
=>1 man = 2 boys
=> 15 men + 6 boys
= 30 boys + 6 boys = 36 boys
=>M1D1 =M2D2
=>24 × 66 = 36 × D2
D2 =$$\frac{24*66}{36}$$ = 44 days.

Ans .

(3) 100 days

1. Explanation :

(3) A, B and C together complete the work in 40 days.
(A + B + C)s 1 days work = $$\frac{1}{40}$$
(A + B + C)s 16 days work=$$\frac{16}{40}$$=$$\frac{2}{5}$$
Remaining Work = 1-$$\frac{2}{5}$$=$$\frac{3}{5}$$
This part of work is done by B and C in 40 days.
=>Time taken in doing $$\frac{3}{5}$$ work = 40 days. =>Time taken in doing in 1 work = $$\frac{40 *5}{3}$$=$$\frac{200}{3}$$days.
As days work = (A + B + C)s 1 days work - (B + C)s 1 days work = $$\frac{1}{40}$$+ $$\frac{3}{200}$$=$$\frac{5-3}{200}$$= $$\frac{2}{200}$$= $$\frac{1}{100}$$
Required time = 100 days.

Ans .

(2)40

1. Explanation :

(2) Number of men originally = x (let)
=>M1D1=M2D2
=> × 60 = (x + 8) × 50
=>6x = 5x + 40
=>6x – 5x = 40
=>x = 40 men

Ans .

(4) 60

1. Explanation :

(4) Using Rule 1,,
Number of men originally = x (let)
=>M1D1=M2D2
=> x × 18 = (x – 6) × 20
=>x × 9 = (x – 6) × 10
= 10x – 60
=>10x – 9x = 60
=> x = 60 men

Ans .

(4)75

1. Explanation :

(4) Original number of men= x (let)
=>M1D1=M2D2
=>x × 40 = (x + 45) × 25
=>8x = (x + 45) × 5
=>8x = 5x + 225
=> 8x – 5x = 225
=> 3x = 225
=> x= $$\frac{225}{3}$$= 7 men.

Ans .

(2) 9 days

1. Explanation :

(2) Let A left the work after x days.
According to the question,
Work done by A in x days + work done by B in (23 + x ) days = 1
=> $$\frac{x}{45}$$ +$$\frac{23+x}{40}$$=1
=>$$\frac{8x+207+9x}{360}$$ = 1
=>17x + 207 = 360
=> 17x = 360 – 207 = 153
=> x = $$\frac{153}{17}$$ = 9days.

Ans .

(2) 12

1. Explanation :

Ans .

(4) 11

1. Explanation :

(4) Let the work be completed in x days.
According to the question,
C worked for (x – 4) days.
= $$\frac{x}{24}$$ +$$\frac{x}{30}$$=$$\frac{x-4}{40}$$=1
=>$$\frac{5x+4x+3(x-4)}{120}$$ =1
=>$$\frac{12x-12}{120}$$ = 1
=>$$\frac{12(x-1)}{120}$$= 1
=>$$\frac{x-1}{10}$$ =>x – 1 = 10
=> x = 10 + 1 = 11 days.

Ans .

(2)24

1. Explanation :

(2) (A + B)s 1 days work = $$\frac{1}{15}$$....(i)
(B + C)s 1 days work = $$\frac{1}{12}$$ .... (ii) and (C + A)s 1 days work = $$\frac{1}{10}$$.... (iii)
On adding all three equations, 2 (A + B + C)’s 1 days work = $$\frac{1}{15}$$+$$\frac{1}{12}$$+$$\frac{1}{10}$$
=$$\frac{4+6+5}{60}$$ =$$\frac{15}{60}$$ = $$\frac{1}{4}$$
(A + B + C)s 1 days work = $$\frac{1}{8}$$....(iv)
By equation (iv) – (ii), As 1 days work = $$\frac{1}{8}$$- $$\frac{1}{12}$$ = $$\frac{3-2}{24}$$ = $$\frac{1}{24}$$
Required time = 24 days.

Ans .

(2)24

1. Explanation :

(2) Number of men initially = x (let)
=>M1D1=M2D2
=> x × 40 = (x + 8) × 30
=>4x = 3x + 24
=>4x – 3x = 24
=>x = 24 men

Ans .

(3) 36 days

1. Explanation :

(3) Let Y alone complete the work in x days.
According to the question,
Xs 16 days work + Ys 12 days work = 1
=> $$\frac{16}{24}$$ +$$\frac{12}{x}$$ =1
=>$$\frac{2}{3}$$ +$$\frac{12}{x}$$ =1
=>$$\frac{12}{x}$$ = 1 -$$\frac{2}{3}$$ =$$\frac{1}{3}$$
=>x = 12 × 3 = 36 days

Ans .

(3)40 days

1. Explanation :

Ans .

(2)1$$\frac{2}{3}$$days

1. Explanation :

(2) Work done by A and B in 5 =5($$\frac{1}{10}$$+$$\frac{1}{15}$$) =5($$\frac{3+2}{30}$$)
= 5*$$\frac{5}{30}$$ =$$\frac{5}{6}$$
Remaining Work = 1- $$\frac{5}{6}$$ =$$\frac{1}{6}$$
Time taken by A =$$\frac{1}{6}$$*10 = $$\frac{5}{3}$$ days.=1$$\frac{2}{3}$$ days.

Ans .

(4)60 days

1. Explanation :

(4) (A + B)’s 1 day’s work = $$\frac{1}{30}$$
(A + B)s 20 days’ work =$$\frac{20}{30}$$ =$$\frac{2}{3}$$
Remaining Work =1- $$\frac{2}{3}$$ =$$\frac{1}{3}$$
Time taken by A in doing $$\frac{1}{3}$$ of work = 20 days
Time taken by A in doing whole work = 3 × 20 = 60 days

Ans .

(4)4 days

1. Explanation :

(4) Nuts cut by Ram and Hari in 1 day =$$\frac{12}{2}$$kg. = 6 kg. ....(i)
Nuts cut by them in 5 days = 30 kg.
Amount of nuts cut by Ram alone = 58 – 30 = 28 kg.
Time = 8 days
Nuts cut by Ram in 1 day =$$\frac{28}{8}$$ = 3.5 kg.
From equation (i),
Nuts cut by Hari in 1 day = (6 – 3.5) kg. = 2.5 kg.
Time taken by Hari in cutting 10 kg. of nuts = $$\frac{10}{2.5}$$= 4 days

Ans .

(4)30 days

1. Explanation :

(4) Rameshs 1 days work =$$\frac{1}{20}$$
Rahmans 1 days work = $$\frac{1}{25}$$
(Ramesh + Rahman)s 1 days work = $$\frac{1}{20}$$+$$\frac{1}{25}$$= $$\frac{5+4}{100}$$=$$\frac{9}{100}$$
Their 10 days work =$$\frac{90}{100}$$=$$\frac{9}{10}$$
Remaininf Work = 1- $$\frac{9}{10}$$ =$$\frac{1}{10}$$
Suresh does$$\frac{1}{10}$$ work in 3 days.
Time taken by Suresh in doing 1 work = 3 × 10 = 30 days

Ans .

(3) 40 days

1. Explanation :

(3) Let C alone complete the work in x days.
According to the question,
As 7 days work + Bs 3 days work + Cs 2 days work = 1
=> $$\frac{7}{10}$$+$$\frac{3}{12}$$+$$\frac{2}{x}$$ =1
=>$$\frac{2}{x}$$= 1 -$$\frac{7}{10}$$-$$\frac{1}{4}$$
=>$$\frac{20-14-5}{20}$$ =$$\frac{1}{20}$$
=> x = 2 × 20 = 40 days.

Ans .

(2) 12

1. Explanation :

(2) Let the number of working men be x.
=> M1D1=M2D2
=> x × 60 = (x + 6) × 40

=> 3x = 2x + 12
=> 3x – 2x = 12
=> x = 12

Ans .

(4) 12 days

1. Explanation :

. (4) As 1 days work =$$\frac{1}{20}$$
Bs 1 days work =$$\frac{1}{15}$$
(A + B + C)s 1 days work =$$\frac{1}{5}$$
Cs 1 days work =$$\frac{1}{5}$$-$$\frac{1}{20}$$-$$\frac{1}{15}$$
=$$\frac{12-3-4}{60}$$=$$\frac{5}{60}$$=$$\frac{1}{12}$$
Required time = 12 days.

Ans .

(3)30

1. Explanation :

. (3) Let 5 men leave the work after x days.
=>M1D1=M2D2+M3D3
=>15 × 40 = 15 × x + 10 × (45 – x)
=> 600 = 15x + 450 – 10x
=> 600 – 450 = 5x
=> 5x = 150
=> x =$$\frac{150}{5}$$= 30 days.

Ans .

(1)24days

1. Explanation :

(1)(A + B)s 1 days work =$$\frac{1}{12}$$
(A + B)’s 5 days’ work = $$\frac{5}{12}$$
Remaining work = 1- $$\frac{5}{12}$$ = $$\frac{7}{12}$$
A does$$\frac{7}{12}$$ work in 14 days.
A will do 1 work in =$$\frac{14*12}{7}$$= 24 days.

# TYPE-III

Ans .

(2) 4 days

1. Explanation :

(3) According to question, (6M + 8B)10 = (26M + 48B)2
60M + 80B = 52M + 96B or, 1M = 2B ; 5M + 20B = (30 + 20)B = 50 boys and 6M + 8B => (12 + 8) boys = 20 boys
20 boys can finish the work in 10 days, 50 boys can finish the work in $$\frac{20*10}{50}$$ days = 4 days

Ans .

(2) 5 days

1. Explanation :

(2) 5*6 men = 10*5 women => 3 men = 5 women;
5 women + 3 men = 6 men; 5 men complete the work in 6 days
6 men will complete the work in $$\frac{5*6}{6}$$ = 5 days.

Ans .

(3) 3 days

1. Explanation :

. (3) 3m = 6w => 1m = 2w; 12m + 8w = (12*2w) + 8w = 32w;
6 women can do the work in 16 days
32 women can do the work in $$\frac{16*6}{32}$$ = 3 days

Ans .

(4) 41 days

1. Explanation :

. (4) 1 mans 1 days work = $$\frac{1}{3}$$ 1 womans 1 days work = $$\frac{1}{4}$$
1 boys 1 days work = $$\frac{1}{4}$$
(1 man + 1 woman)s days work = $$\frac{1}{4}$$*[$$\frac{1}{3}$$ + $$\frac{1}{4}$$] =$$\frac{7}{48}$$
Remaining work = 1-$$\frac{7}{48}$$=$$\frac{41}{48}$$. Now;
1 boys $$\frac{1}{4}$$ days work = $$\frac{1}{4}$$*$$\frac{1}{12}$$= $$\frac{1}{48}$$
$$\frac{41}{48}$$ work will be done by $$\frac{41}{48}$$*48 = 41 boys

Ans .

(4) 10 days

1. Explanation :

4) 16 men = 20 women => 4 men = 5 women. Now, according to question, 16 men complete the work in 25 days.
1 man one days work = $$\frac{1}{25*16}$$ => 4 men one days work = $$\frac{4}{25*16}$$ = $$\frac{1}{100}$$. Similarly,
1 woman one days work = $$\frac{1}{25*20}$$ => 5 women one days work = $$\frac{5}{25*20}$$ = $$\frac{1}{100}$$ => 28 men
= $$\frac{28}{4}$$*5 = 35 women => [28 men + 15 women] => 50 women one days work = $$\frac{50}{25*20}$$ = $$\frac{1}{10}$$
Therefore, 28 men and 15 women can complete the whole work in 10 days.

Ans .

(3) 13$$\frac{1}{3}$$ days

1. Explanation :

(3) According to the question, 5 men = 8 women
2 men = $$\frac{8}{5}$$*2 = $$\frac{16}{5}$$
Total women = $$\frac{16}{5}$$+4 = $$\frac{36}{5}$$
No. of days to do the same work = $$\frac{8*12*5}{36}$$ = $$\frac{40}{3}$$ = 13$$\frac{1}{3}$$

Ans .

(4) 12 days

1. Explanation :

(4) 3 men = 4 women
1 man = $$\frac{4}{3}$$ women
7 men = $$\frac{7*4}{3}$$ = $$\frac{28}{3}$$
7 men + 5 women = $$\frac{28}{3}$$+5 = $$\frac{28+15}{3}$$ = $$\frac{43}{3}$$ Women
Now, M1D1 = M2D2 => 4 * 43 = $$\frac{43}{3}$$*D2, where D2 = number of days
=> D2 = $$\frac{4*3*43}{43}$$ = 12 days.

Ans .

(3) 15 days

1. Explanation :

(3) 6 men = 12 women
1 man = 2 women
Now, 8 men + 16 women = (8*2*16) women = 32 women
12 women can do a work in 20 days. 32 women can do the twice work in $$\frac{20*12*2}{32}$$ = 15 days.

Ans .

(1) 9 days

1. Explanation :

(1) Work done by 1 woman in 1
day = $$\frac{1}{3}$$-$$\frac{1}{6}$$-$$\frac{1}{18}$$ = $$\frac{6-3-1}{18}$$ = $$\frac{1}{9}$$
Woman will do the work in 9 days.

Ans .

(3) 3 mens work = 5 womens work
1 mans work = $$\frac{5}{3}$$ womens work
6 mens work = $$\frac{5}{3}$$*6 = 10 womens work
6 men + 5 women = 15 women
5 women can do work in 12 days.
Hence, 15 women can do it in $$\frac{5*12}{15}$$ = 4 days.

Ans .

(2) 204 days

1. Explanation :

(1) 10 men = 20 boys
1 man = 2 boys
8 men + 4 boys = (16 + 4) boys = 20 boys
Hence, 8 men and 4 boys will make 260 mats in 20 days.

Ans .

(2) 2 days

1. Explanation :

(2) Work done in two days = $$\frac{1}{6}$$*2
= $$\frac{1}{3}$$ , remaining work = $$\frac{2}{3}$$
=> $$\frac{M1D1}{W1}$$ = $$\frac{M2D2}{W2}$$
=> $$\frac{3*2*3}{1}$$ = $$\frac{6*D2*3}{2}$$
=> D2 = $$\frac{3*2*2}{6}$$ = 2 days

Ans .

(3) 40 days

1. Explanation :

(3) Work done by 1 woman in 1 day
= $$\frac{1}{8}$$-$$\frac{1}{10}$$ = $$\frac{5-4}{40}$$-$$\frac{1}{40}$$
One woman will complete the work in 40 days.

Ans .

(3) 40 days

1. Explanation :

(3) Let 1 mans 1 days work = x and 1 womans 1 days work = y
Then, 4x + 6y = $$\frac{1}{8}$$ and
3x+7y = $$\frac{1}{10}$$ br/> From both equations, we get y = $$\frac{1}{400}$$
10 womens 1 days work = $$\frac{10}{400}$$ = $$\frac{1}{40}$$
10 women will finish the work in 40 days.

Ans .

(1) 8 days

1. Explanation :

(1) Part of work done by 2 men and 2 women in 2 days.
= 2[$$\frac{2}{20}$$+$$\frac{8}{30}$$]
= 2[$$\frac{1}{10}$$+$$\frac{8}{30}$$] = 2$$\frac{3+8}{30}$$
= $$\frac{22}{30}$$ = $$\frac{11}{15}$$
Remaining work = 1-$$\frac{11}{15}$$ = $$\frac{4}{15}$$
Work done by 1 boy in 2 days = $$\frac{2}{60}$$ = $$\frac{1}{30}$$
Number of boys required to assist = $$\frac{4}{15}$$*30 = 8

Ans .

(3) 48 days

1. Explanation :

(3) 1 man = 2 women = 3 boys
1 man + 1 woman + 1 boy = [3+$$\frac{3}{2}$$+1] boys = $$\frac{11}{2}$$ boys
M1D1 = M2D2
=> 3*88 = $$\frac{11}{2}$$*D2
=> D2= $$\frac{2*3*88}{11}$$ = 48 days

Ans .

(2) 20 days

1. Explanation :

(2) 6m + 8w = 10 days
=> 2*(3m + 4w) = 10 days
=> 3m + 4w = 20 days
[Since the workforce has become half of the original force, so number of days must be double].

Ans .

(1) 17$$\frac{1}{2}$$ days

1. Explanation :

(1) 12*(3 men + 4 boys) = 10*(4 men + 3 boys)
=> 36 men + 48 boys = 40 men + 30 boys => 4 men = 18 boys => 2 men = 9 boys
4 men + 3 boys = 21 boys, who do the work in 10 days and 2 men + 3 boys = 12 boys
M1D1 = M2D2
=> 21*10 = 12*D2
=> D2 = $$\frac{21*10}{12}$$ = $$\frac{35}{2}$$ = 17$$\frac{1}{2}$$ days.

Ans .

(4) 8 months

1. Explanation :

(4) 10 men = 20 women
1 man = 2 women = 5 children
1 woman = 2 children
5 men + 5 women + 5 children = 20 + 10 + 5 = 35 children
M1D1 = M2D2
40*7 = 35*D2
D2 = $$\frac{40*7}{35}$$ = 8 months
5 men, 5 women and 5 children can do half of the work in 8 months
Required time = 4 months.

Ans .

(1) 5$$\frac{1}{3}$$ days

1. Explanation :

(1) 8 men = 12 boys
4 men = 6 boys
=> 20 men = 30 boys
=> 20 men + 6 boys = 36 boys
M1D1 = M2D2
=> 12*16 = 36*D2
D2 = $$\frac{12*16}{36}$$= $$\frac{16}{3}$$ = 5$$\frac{1}{3}$$ days.

Ans .

(3) 12$$\frac{1}{2}$$ days

1. Explanation :

(3) According to the question, 20 men + 30 boys = 24 men + 16 boys
4 men = 14 boys
=> 2 men = 7 boys
=> 2 men + 1 boy = 8 boys
=>2 men + 3 boys = 10 boys
By M1D1 = M2D2
=> 10*10 = 8*D2
=> D2 = $$\frac{10*10}{8}$$ = $$\frac{25}{2}$$
= 12$$\frac{1}{2}$$ days

Ans .

(2) 12$$\frac{1}{2}$$ days

1. Explanation :

(2) 2*10 men + 3*10 women
= 3*8 men + 2*8 women
=> 20 men + 30 women
= 24 men + 16 women
=> 4 men = 14 women
or 2 men = 7 women
2 men + 3 women = 10 women
2 men + 1 woman = 8 women
M1D1 = M2D2
=> 10*10 = 8*D2
=> D2 = $$\frac{25}{2}$$ = 12$$\frac{1}{2}$$ days

Ans .

(1) 17$$\frac{1}{2}$$ days

1. Explanation :

(1) 12*(3 men + 4 boys) = 10*(4 men + 3 boys)
=> 36 men + 48 boys = 40 men + 30 boys => 4 men = 18 boys or 2 men = 9 boys
4 men + 3 boys = 21 boys who do the work in 10 days and, 2 men + 3 boys = 12 boys
M1D1 = M2D2
=> 21*10 = 12*D2
=>D2 = $$\frac{21*10}{12}$$ = $$\frac{35}{2}$$ = 17$$\frac{1}{2}$$ days

Ans .

(2) 7 days

1. Explanation :

(2) Using Rule 1, 4 men = 6 women
1 men = $$\frac{6}{4}$$ = $$\frac{3}{2}$$ women
10 men + 3 women = 10$$\frac{3}{2}$$+3 = 18 women
$$\frac{M1D1T1}{W1}$$ = $$\frac{M2D2T2}{W2}$$
=> $$\frac{6*12*7}{1}$$ = $$\frac{18*D2*8}{W2}$$
=> D2 = $$\frac{6*12*7*2}{18*8}$$ = 7 days

Ans .

(3) 40 days

1. Explanation :

(3) Time taken by boy = x days
$$\frac{1}{10}$$+$$\frac{1}{24}$$+$$\frac{1}{x}$$ = $$\frac{1}{6}$$
=> $$\frac{1}{x}$$ = $$\frac{1}{6}$$+$$\frac{1}{10}$$+$$\frac{1}{24}$$
= $$\frac{20-12-5}{120}$$ = $$\frac{3}{120}$$ = $$\frac{1}{40}$$
=> x = 40 days

Ans .

(3) 5$$\frac{7}{13}$$ months

1. Explanation :

(3) 40 men = 60 women º=80 children
10 men = $$\frac{80}{40}$$*10
= 20 children
10 women = $$\frac{80}{60}$$*10
= $$\frac{40}{3}$$ children
10 men + 10 women + 10 children
= [20+$$\frac{40}{3}$$+10] children
= $$\frac{60+40+30}{3}$$ children
= $$\frac{120}{3}$$ children
$$\frac{M1D1}{W1}$$ = $$\frac{M2D2}{W2}$$
D2 = $$\frac{80*6*13}{130}$$ = $$\frac{144}{13}$$ months
Half of the work can do
= $$\frac{144}{13}$$*$$\frac{1}{2}$$ = $$\frac{72}{13}$$ = 5$$\frac{7}{13}$$ months

Ans .

(1) 49

1. Explanation :

(1) Using Rule 11,
According to the question,
1 man = 2 women = 4 boys
1 man + 1 woman + 1 boy
= (4+2+1) boys = 7 boys
M1D1 = M2D2
=> 7*7 = 1*D2
=> D2 = 49 days

Ans .

(3) 48 days

1. Explanation :

(3) 1 man = 2 women = 3 boys
1 man + 1 woman + 1 boy
= [3+$$\frac{3}{2}$$+1] boys
= $$\frac{6+3+2}{2}$$
= $$\frac{11}{2}$$
M1D1 = M2D2

3*88 = $$\frac{11}{2}$$*D2
D2= $$\frac{3*2*88}{11}$$ = 48 days

Ans .

(2) 21 days

1. Explanation :

(2) 3 men = 7 women
7 men = $$\frac{7*7}{3}$$
= $$\frac{49}{3}$$ women
7 men + 5 women
= [$$\frac{49}{3}$$+5] women
= $$\frac{49+15}{3}$$ women
= $$\frac{64}{3}$$ women
$$\frac{M1D1}{W1}$$ = $$\frac{M2D2}{W2}$$
=> $$\frac{7*32}{1}$$ = $$\frac{64*D2}{3*2}$$
=> D2 = $$\frac{7*32*3*2}{64}$$ = 21 days

Ans .

(2) 24 days

1. Explanation :

(2) 1 man = 2 women = 3 boys
1 man + 1 woman + 1 boy
= 3 boys + $$\frac{3}{2}$$ boys + 1 boy = $$\frac{11}{2}$$ boys
By M1D1 = M2D2
3*44 = $$\frac{11}{2}$$*D2
=> D2 = $$\frac{2*3*44}{11}$$ = 24 days

Ans .

(3) 12 days

1. Explanation :

(3) Using Rule 1,
2 children = 1 man
8 children + 12 men = 16 men
M1D1 = M2D2 ,
16*9 = 12*D2
D2 = $$\frac{16*9}{12}$$ = 12 days.

Ans .

(1) 2:1

1. Explanation :

(1) Work done by 12 men + 16 boys in 5 days
= Work done 13 men + 24 boys in 4 days
=> (60 men + 80 boys)s 1 days work = (52 men + 96 boys)s 1 days work
=> (60 - 52) men = (96 -80) boys
=> 8 men = 16 boys
=> 1 man = 2 boys
Required ratio = 2 : 1

Ans .

(2) 4:3

1. Explanation :

(2) 20 women complete 1 work in 16 days
16 men complete same work in 15 days
16*15 men = 20*16 women
=> 3 men = 4 women
Required ratio = 4:3

Ans .

(4) 8

1. Explanation :

(4) 18 men = 36 boys
=> 1 man = 2 boys
24 men + 24 boys
= (24 + 12) men
= 36 men
M1D1T1 = M2D2T2
=> 18*24*6 = 36*D2*9
=> D2= $$\frac{1}{72}$$ = 8 days

Ans .

(3) 10 days

1. Explanation :

(3) 5 men can do 1 work in 14 days.
3 men will do $$\frac{3}{5}$$ work in 14 days.
Remaining work = 1-$$\frac{3}{5}$$ - $$\frac{2}{5}$$
5 men will do $$\frac{2}{5}$$ work in 14 days.
Time taken by 5 women in doing 1 work
= $$\frac{14*5}{2}$$ = 35 days
(5 men + 5 women)s 1 days work
= $$\frac{1}{14}$$+$$\frac{1}{35}$$ = $$\frac{5+2}{70}$$ = $$\frac{7}{70}$$ = $$\frac{1}{10}$$
Required time = 10 days.

# TYPE-IV

Ans .

(1) $$\frac{8}{15}$$

1. Explanation :

(1) Using basics of Rule 2,
As work per day = $$\frac{1}{15}$$
Bs work per day = $$\frac{1}{20}$$
(A+ B)s work per day
= $$\frac{1}{15}$$+$$\frac{1}{20}$$ = $$\frac{4+3}{60}$$ = $$\frac{7}{60}$$
(A + B)s work in 4 days
= 4*$$\frac{7}{60}$$ = $$\frac{7}{15}$$
Left work = 1-$$\frac{7}{15}$$ = $$\frac{15-7}{15}$$ = $$\frac{8}{15}$$

Ans .

(3) 8 days

1. Explanation :

(3) Using basics of Rule 2,
The part of field cultivated by A in 1 day
= $$\frac{2}{5*6}$$ = $$\frac{1}{15}$$
The part of field cultivated by B in 1 day
= $$\frac{1}{3*10}$$ = $$\frac{1}{30}$$
The part of field cultivated by A and B together
= $$\frac{1}{15}$$+$$\frac{1}{30}$$ = $$\frac{3}{30}$$ = $$\frac{1}{10}$$
$$\frac{4}{5}$$ part of field cultivated by A and B together in
$$\frac{40}{5}$$ days = $$\frac{4*10}{5}$$ = 8 days

Ans .

(1) 37$$\frac{1}{2}$$ days

1. Explanation :

(1) Using basics of Rule 2,
A can do the whole work in
$$\frac{20*5}{4}$$ = 25 days
Remaining work = 1-$$\frac{4}{5}$$ = $$\frac{1}{5}$$
(A + B)s 1 days work = $$\frac{1}{15}$$
As 1 days work = $$\frac{1}{25}$$
Bs 1 days work
= $$\frac{1}{15}$$-$$\frac{1}{25}$$ = $$\frac{5-3}{75}$$ = $$\frac{2}{75}$$
B can finish the work in $$\frac{75}{2}$$
days i.e., 37 $$\frac{1}{2}$$ days

Ans .

(1) $$\frac{1}{6}$$

1. Explanation :

(1) Using basics of Rule 2,
As 1 days work = $$\frac{1}{18}$$
Bs 1 days work = $$\frac{1}{9}$$ /
(A+B)s 1 days work
= $$\frac{1}{18}$$+$$\frac{1}{69}$$ = $$\frac{1+2}{18}$$ = $$\frac{3}{18}$$ = $$\frac{1}{6}$$

Ans .

(3) 13$$\frac{1}{3}$$

1. Explanation :

(3) Using basics of Rule 2,
Remaining work
= 1-$$\frac{7}{10}$$ = $$\frac{3}{10}$$
(A + B) take 4 days to do $$\frac{3}{10}$$ work
(A + B) will do the work in 4$$\frac{10}{3}$$ days
= $$\frac{40}{3}$$ = 13$$\frac{1}{3}$$ days

Ans .

(2) $$\frac{2}{3}$$

1. Explanation :

(2) Using basics of Rule 2,
Time taken by A and B
= $$\frac{6*12}{6+12}$$ = $$\frac{6*12}{18}$$ = 4
Work done by A in 4 days
= $$\frac{4}{6}$$ = $$\frac{2}{3}$$

Ans .

(4) Using basics of Rule 3,
A can do $$\frac{1}{2}$$ work in 5 days.
A can do 1 work in 10 days
Similarly,
B can do 1 work in $$\frac{5}{3}$$*9
= 15 days.
C can do 1 work in 8*$$\frac{3}{2}$$ = 12 days.
Now,
As 1 days work = $$\frac{1}{10}$$
Bs 1 days work = $$\frac{1}{15}$$
Cs 1 days work = $$\frac{1}{12}$$
(A + B + C)s 1 days work
= $$\frac{1}{10}$$+$$\frac{1}{15}$$+$$\frac{1}{12}$$
= $$\frac{6+4+5}{60}$$ = $$\frac{15}{60}$$ = $$\frac{1}{4}$$
Hence, (A + B + C) together can complete the work in 4 days.

Ans .

(3) 4 days

1. Explanation :

(3) Using basics of Rule 1,

$$\frac{7}{8}$$: $$\frac{7}{8}$$ :: 28: x
where x is no. of men
=> $$\frac{7}{8}$$*x = $$\frac{1}{8}$$*28
=> x = $$\frac{28*8}{7*8}$$ = 4

Ans .

(2) 9$$\frac{3}{8}$$ days

1. Explanation :

(2) Using basics of Rule 2,
Time taken by A alone in doing
the work = 15 days
Time taken by B alone in doing
the work =
$$\frac{10*5}{2}$$ = 25 days
(A + B)s 1 days work
= $$\frac{1}{15}$$+$$\frac{1}{25}$$ = $$\frac{5+3}{75}$$ = $$\frac{8}{75}$$
Hence, the work will be completed
in $$\frac{75}{8}$$ = 9*$$\frac{3}{8}$$ days

Ans .

(3) 3$$\frac{3}{4}$$

1. Explanation :

(3) Using basics of Rule 2,
Time taken by A to complete the
work = $$\frac{3}{4}$$ = 6 days
Time taken by B to complete the
work = $$\frac{6*5}{3}$$ = 10 days
(A + B)s 1 days work
= $$\frac{1}{6}$$+$$\frac{1}{10}$$ = $$\frac{5+3}{30}$$ = $$\frac{8}{30}$$ = $$\frac{4}{15}$$
A and B together will complete
the work in $$\frac{15}{4}$$ = 3*$$\frac{3}{4}$$ days

Ans .

(2) 20

1. Explanation :

(2) Using basics of Rule 1,

=> 30*$$\frac{3}{4}$$*x = 60*$$\frac{1}{4}$$*60
=> x = $$\frac{60*60}{30*3}$$ = 40
20 men should be discharged.

Ans .

(2) Q

1. Explanation :

(2) Time taken by P in completing
1 work = 10*4 = 40 days
Time taken by Q in completing 1
work = $$\frac{15*5}{2}$$ = $$\frac{75}{2}$$ days
Time taken by R in completing 1
work = 13*3 = 39 days
Time taken by S in completing 1
work = 7*6 = 42 days
Clearly, Q took the least time i.e. $$\frac{75}{2}$$ or 35$$\frac{1}{2}$$ days.

Ans .

(3) $$\frac{1}{20}$$

1. Explanation :

(3) Using basics of Rule 5,
(A + B)s 1 days work = $$\frac{1}{72}$$
(B + C)s 1 days work = $$\frac{1}{120}$$
(C + A)s 1 days work = $$\frac{1}{60}$$
On adding all three, 2(A + B + C)s 1 days work
= $$\frac{1}{72}$$+$$\frac{1}{120}$$+$$\frac{1}{60}$$ = $$\frac{5+3+4}{360}$$ = $$\frac{1}{30}$$
(A + B + C)s 1 days work = $$\frac{1}{60}$$
(A + B + C)s 3 days work = $$\frac{3}{60}$$ = $$\frac{1}{20}$$

Ans .

(1) 12 days

1. Explanation :

(1) Using basics of Rule 2,
Time taken by A to finish the work
= 5*6 = 30 days
Time taken by B to complete the
work = $$\frac{8*5}{2}$$ = 20 days
(A + B)s 1 days work
= $$\frac{1}{30}$$+$$\frac{1}{20}$$ = $$\frac{2+3}{60}$$ = $$\frac{1}{12}$$
Required time = 12 days

Ans .

(1) $$\frac{5}{8}$$

1. Explanation :

(1) Using basics of Rule 2,
(A + B)s 5 days work
= 5*[$$\frac{1}{20}$$+$$\frac{1}{40}$$]
= 5*$$\frac{2+1}{40}$$ = $$\frac{15}{40}$$ = $$\frac{3}{8}$$
Remaining work = 1-$$\frac{3}{8}$$ = $$\frac{5}{8}$$

Ans .

(4) 6 days

1. Explanation :

(4) (A+B)s 1 days work
= $$\frac{1}{20}$$+$$\frac{1}{30}$$ = $$\frac{3+2}{60}$$ = $$\frac{1}{12}$$
Work done in 6 days
= $$\frac{6}{12}$$ = $$\frac{1}{2}$$

Ans .

(1) 30 days

1. Explanation :

(1) Using basics of Rule 2,
Let B completes the work in x days.
Work done by A in $$\frac{3x}{4}$$ days = $$\frac{1}{2}$$
=> Time taken by A in completing
the work = 2*$$\frac{3x}{4}$$ = $$\frac{3x}{2}$$ days
(A + B)s 1 days work
= $$\frac{1}{x}$$+$$\frac{2}{3x}$$ = $$\frac{3+2}{3x}$$ = $$\frac{5}{3x}$$
$$\frac{5}{3x}$$ = $$\frac{1}{18}$$ => 3x = 90
=> x = 30
Hence, time taken by B in completing
the work = 30 days

Ans .

(2) 25 days

1. Explanation :

(2) Using basics of Rule 2,
If B completes a work in x days,
A will complete the same in
$$\frac{2x}{3}$$ days.
$$\frac{1}{x}$$+$$\frac{3}{2x}$$ = $$\frac{1}{10}$$
=> $$\frac{2+3}{2x}$$ = $$\frac{1}{10}$$ => 2x = 50
=> x = 25 days

Ans .

(4) 7$$\frac{1}{5}$$ days

1. Explanation :

(4) Using basics of Rule 2,
Ratio of efficiency of A and B
= 3:2
Ratio of time taken = 2:3
Time taken by A
= $$\frac{2}{3}$$*18 = 12 days
(A + B)s 1 days work
= $$\frac{1}{12}$$+$$\frac{1}{18}$$ = $$\frac{3+2}{36}$$ = $$\frac{5}{36}$$
Required time
= $$\frac{36}{5}$$ = 7*$$\frac{1}{5}$$ days

Ans .

(4) 13$$\frac{5}{7}$$ days

1. Explanation :

(4) Using basics of Rule 2,
A does $$\frac{7}{8}$$ work in 28 days.
A will complete the work in
28*$$\frac{8}{7}$$ = 32 days
B does $$\frac{5}{6}$$ work in 20 days.
B will complete the work in
$$\frac{20*6}{5}$$ = 24 days
(A + B)s 1 days work
= $$\frac{1}{32}$$+$$\frac{1}{24}$$ = $$\frac{3+4}{96}$$ = $$\frac{7}{96}$$
Required time
= $$\frac{96}{7}$$ = 13$$\frac{5}{7}$$ days

Ans .

(4) 13$$\frac{5}{7}$$ days

1. Explanation :

(4) Time taken by A and B = x
hours (let).
According to the question,
Time taken by A alone
= (x + 8) hours.
Time taken by B alone
= [x+$$\frac{9}{2}$$] days
$$\frac{1}{x+8}$$+$$\frac{2}{x+9}$$ = $$\frac{1}{x}$$
=> $$\frac{1}{x+8}$$+$$\frac{2}{2x+9}$$ = $$\frac{1}{x}$$
=> $$\frac{2x+9+2x+16}{(x+8)*(2x+9)}$$ = $$\frac{1}{x}$$
=> 4x+25 / 2x2+16x+9x+72 = $$\frac{1}{x}$$
=> 4x2+25x = 2x2+25x+72
=> 2x2 = 72 => 2x2 = $$\frac{72}{2}$$ = 36
=> x = 6 hours

Ans .

(1) 100

1. Explanation :

Ans .

(2) 9$$\frac{3}{5}$$ days

1. Explanation :

(2) Using basics of Rule
x does $$\frac{1}{4}$$ work in 6 days
x does 1 work in 24 days
Similarly,
y does $$\frac{3}{4}$$ work in 12 days
y does 1 work in $$\frac{12*4}{3}$$
= 16 days
(x + y)s 1 days work
= $$\frac{1}{24}$$+$$\frac{1}{16}$$ = $$\frac{2+3}{48}$$ = $$\frac{5}{48}$$
Required time = $$\frac{48}{5}$$
= 9*$$\frac{3}{5}$$ days

Ans .

(4) 30 days

1. Explanation :

(4) Let the time taken by B in
doing the work alone = x days
According to the question,
Time taken by A
= 2*$$\frac{3x}{4}$$ = $$\frac{3x}{2}$$ days
$$\frac{1}{x}$$+$$\frac{2}{3x}$$= $$\frac{1}{18}$$
=> $$\frac{1}{x}$$+$$\frac{2}{3x}$$ = $$\frac{1}{18}$$
=> $$\frac{3+2}{3x}$$ = $$\frac{1}{18}$$
=> 3x = 18*5
=> x = $$\frac{18*5}{3}$$ = 30 days

Ans .

(2) Rs. 3,450

1. Explanation :

(2) Part of work done by A and
B = $$\frac{19}{23}$$
Part of work done by C
= 1-$$\frac{19}{23}$$ = $$\frac{4}{23}$$
Part of work done by B and C
= $$\frac{8}{23}$$
Part of work done by B
= $$\frac{8}{23}$$-$$\frac{4}{23}$$ = $$\frac{4}{23}$$
Part of work done by A
= $$\frac{19}{23}$$-$$\frac{4}{23}$$ = $$\frac{15}{23}$$
Ratio of the shares of wages of
A, B and C
= $$\frac{15}{23}$$ : $$\frac{4}{23}$$ : $$\frac{4}{23}$$ = 15:4:4
As share
= $$\frac{15}{23}$$*5290 = Rs. 3450

Ans .

(4) 3$$\frac{1}{4}$$

1. Explanation :

(4) Using basics of Rule 2
Work done by A and B in 1 day
= $$\frac{1}{10}$$+$$\frac{1}{20}$$ = $$\frac{2+1}{20}$$ =$$\frac{3}{20}$$
(A + B)s 5 days work
= $$\frac{5*3}{20}$$ = $$\frac{3}{4}$$
Remaining work
= 1-$$\frac{3}{4}$$ = $$\frac{1}{4}$$

Ans .

(2) 5$$\frac{1}{3}$$ days

1. Explanation :

(2) According to the question,
(4*8) men + (6*8) women =
(2*8) men + (9*8) women
=> 4 men + 6 women = 2 men +
9 women
=> (4 - 2) men = (9 - 6) women
=> 2 men = 3 women
4 men + 6 women = 12 women
M1D1 = M2D2
=> 12*8 = 18*D2
=> D2 = $$\frac{12*8}{18}$$ = $$\frac{16}{3}$$ = 5$$\frac{1}{3}$$ days

Ans .

(1) 90 days

1. Explanation :

(1) Let time taken by A alone
in doing work be x days.
Time taken by B alone
= 3x days
A and B together finish $$\frac{2}{5}$$
work in 9 days.
TIme taken by A and B in
doing whole work
= $$\frac{9*5}{2}$$ = $$\frac{45}{2}$$ days
$$\frac{1}{x}$$+$$\frac{1}{3x}$$ = $$\frac{2}{45}$$
=> $$\frac{3+1}{3x}$$ = $$\frac{2}{45}$$
=> $$\frac{4}{3x}$$ = $$\frac{2}{45}$$ => 2*3x = 4*45
=> x = $$\frac{4*45}{2*3}$$ = 30 days
Time taken by B = 3x days
= 3*30 = 90 days

Ans .

(4) 8

1. Explanation :

(4) Using Rule 1,

=> 16*$$\frac{15}{2}$$*x = 12*8*10
=> 8*15*x = 12*8*10
=> x = $$\frac{12*8*10}{8*15}$$ = 8 days

Ans .

(4) 16

1. Explanation :

Ans .

(3) 9 days

1. Explanation :

Ans .

(4) 2$$\frac{8}{11}$$

1. Explanation :

(4) According to the question,
John does $$\frac{1}{2}$$ work in 3 hours.
Time taken by John in doing
whole work = 6 hours
Joe does $$\frac{1}{8}$$ work in 1 hour.
Time taken by Joe in doing
whole work = 8 hours
Remaining work = $$\frac{1}{2}$$-$$\frac{1}{8}$$
= $$\frac{4-1}{8}$$ = $$\frac{3}{8}$$ parts
Time taken by George
= $$\frac{8*5}{3}$$ = $$\frac{40}{3}$$ hours
Work done by all three in 1 hour
= $$\frac{1}{6}$$+$$\frac{1}{8}$$+$$\frac{3}{40}$$
= $$\frac{20+15+9}{120}$$ = $$\frac{44}{120}$$
= $$\frac{11}{30}$$
Required time = $$\frac{30}{11}$$
= 2$$\frac{8}{11}$$ hours

Ans .

(4) 18 days

1. Explanation :

(4) Remaining work = 1-$$\frac{2}{5}$$
= $$\frac{3}{5}$$ parts
(A + B) together do $$\frac{3}{5}$$th part
of work in 6 days.
Time taken by A and B in doing
whole work = $$\frac{6*5}{3}$$
= 10 days
A does $$\frac{2}{5}$$th part of work in 9 days.
Time taken by A in doing whole
work = $$\frac{9*5}{2}$$ = 45 days
Bs 1 days work = $$\frac{1}{10}$$-$$\frac{2}{45}$$
= $$\frac{9-4}{90}$$ = $$\frac{5}{90}$$ = $$\frac{1}{18}$$
Required time = 18 days

Ans .

(1) 20

1. Explanation :

(1) Remaining work
= 1-$$\frac{37}{100}$$
= $$\frac{100-37}{100}$$ = $$\frac{63}{100}$$
Time taken by (A + B) in doing
$$\frac{63}{100}$$ part of work
= 7 days
Time taken by them in doing
whole work = $$\frac{100}{63}$$*7
= $$\frac{100}{9}$$ days
Respective ratio of time taken by
A and B in doing the work
= 5:4
$$\frac{1}{4x}$$+$$\frac{1}{5x}$$ = $$\frac{9}{100}$$
=> $$\frac{5+4}{20x}$$ = $$\frac{9}{100}$$
=> 20x = 100 => x = 5
Required time
= 4*5 = 20 days

Ans .

(4) $$\frac{a-3}{3a}$$

1. Explanation :

(4) Dhiru digs $$\frac{1}{a}$$ part of field
in 20 hours.
Dhiru digs 1 part of field in 20a
hours.
= $$\frac{1}{60}$$-$$\frac{1}{20a}$$ = $$\frac{a-3}{60a}$$
Part of field dug by Kaku in 1
hour
= $$\frac{20(a-3)}{60a}$$ = $$\frac{a-3}{3a}$$

Ans .

(2) 7$$\frac{1}{2}$$ days

1. Explanation :

(2) A can do a work in 12 days.
B is 60% more efficient than A.
Time taken by B
= [$$\frac{100}{160}$$*12] days
= $$\frac{15}{2}$$ = 7$$\frac{1}{2}$$ days

Ans .

(3) 48 days

1. Explanation :

(3) B completes $$\frac{1}{3}$$ work in 12
days.
B will complete 1 work in 12*3 = 36 days.
Bs 1 days work = $$\frac{1}{36}$$
(A + B)s 1 days work = $$\frac{1}{24}$$
A’s 1 days work = $$\frac{1}{24}$$-$$\frac{1}{36}$$
= $$\frac{3-2}{72}$$ = $$\frac{1}{72}$$
Time taken by A in doing 1
work = 72 days
Remaining work = 1-$$\frac{1}{3}$$ = $$\frac{2}{3}$$
Time taken by A in doing $$\frac{2}{3}$$
work = $$\frac{2}{3}$$*72 = 48 days

Ans .

(3) 9$$\frac{3}{8}$$ days

1. Explanation :

(3) A does $$\frac{1}{3}$$rd part of work
in 5 days.
A will do 1 work in 5*3
= 15 days.
B does $$\frac{2}{5}$$th of work in 10
days.
B will do 1 work in $$\frac{10*5}{2}$$ = 25 days
(A + B)s 1 days work
= $$\frac{1}{15}$$+$$\frac{1}{25}$$
= $$\frac{5+3}{75}$$ = $$\frac{8}{75}$$
Required time = $$\frac{75}{8}$$
= 9$$\frac{3}{8}$$ days

Ans .

(4) Rs. 80

1. Explanation :

(4) Work done by A and B together
= $$\frac{9}{11}$$ parts
Work done by C
= 1-$$\frac{9}{11}$$ = $$\frac{2}{11}$$ parts
Total amount = Rs. 440
Cs share = Rs. [$$\frac{2}{11}$$*440]
= Rs. 80

Ans .

(3) R

1. Explanation :

(3) P does $$\frac{1}{4}$$th work in 10
days.
P will do 1 work in 10*4
= 40 days
Q, does 40% part of work in
40 days
Q will do 100% work in
$$\frac{40*100}{40}$$ = 100 days
R, does $$\frac{1}{3}$$rd work in 13 days.
R will do 1 work in 13*3
= 39 days

# TYPE-V

Ans .

(3) 40 days

1. Explanation :

(3) Let B does the whole work in x days
Work done by B in 1 day = $$\frac{1}{x}$$
According to question A does the $$\frac{1}{2}$$ work in $$\frac{x}{6}$$ days
A does the whole work in $$\frac{2x}{6}$$ or $$\frac{x}{13}$$ days Work done by A in one day = $$\frac{3}{x}$$ days.
Work done by A and B together in one day = $$\frac{1}{x}$$ +$$\frac{3}{x}$$ +$$\frac{4}{x}$$
Time taken to complete the whole work by A and B together = $$\frac{0.25}{x}$$ days
Again, given that , $$\frac{x}{4}$$ =10 => x = 40 days.

Ans .

(3) 11 days

1. Explanation :

(3) Ratio of efficiency of Babu and Asha = 1 : $$\frac{7}{4}$$ = 4 : 7.
As the time taken is inversely proportional to efficiency, therefore, if Babu takes 7x days to complete work, Asha will take 4x days.
$$\frac{1}{7x}$$ +$$\frac{1}{4x}$$ =$$\frac{1}{7}$$ =>$$\frac{4+7}{28x}$$ =$$\frac{1}{7}$$
=>28x = 11 * 7
=> x= $$\frac{11*7}{28}$$=$$\frac{11}{4}$$
Asha will complete the work in 4x = 4 *$$\frac{11}{4}$$ = 11 days

Ans .

(2) 8 days

1. Explanation :

(2) Using Rule 1,
Jyothi can do $$\frac{3}{4}$$th of a job in 12 days.
Jyothi can do 1 job in $$\frac{12*4}{3}$$ =16 days.
As Mala is twice as efficient as Jyothi,
Mala will finish the job in 8 days.

Ans .

(3) 50 days

1. Explanation :

(3) A : B = D2 : D1
=>100 : 140 =D2 : 70
=>100 * 70 = 140 * D2
D2 = $$\frac{100*70}{140}$$ =50 days.

Ans .

(4) 8 days

1. Explanation :

Ans .

(1) 30 days

1. Explanation :

(1) Using basics of Rule 2,
Let B alone can do the work in x days.
A can do the work in $$\frac{3x}{2}$$ days.
According to the question, $$\frac{1}{x}$$+ $$\frac{2}{3x}$$= $$\frac{1}{18}$$=> $$\frac{3+2}{3x}$$= $$\frac{1}{18}$$
= >$$\frac{5}{3x}$$ = $$\frac{1}{18}$$ => 3x= 18* 5
=> x =$$\frac{18*5}{3}$$ =30 days.

Ans .

(3) 24 days

1. Explanation :

(3) Using basics of Rule 2,
According to the question,
If A takes x days to complete the work, B will take 2x days and C will take 4x days, Now, (A + B)'s 1 days work = $$\frac{1}{4}$$
=>$$\frac{1}{x}$$+$$\frac{1}{2x}$$=$$\frac{1}{4}$$=>$$\frac{2+1}{2x}$$=$$\frac{1}{4}$$
=> 2x = 12 => x = 6
C will complete the work in 4x i.e. 24 days.

Ans .

(3) 25 days

1. Explanation :

(*) Ratio of the work of A and B done in 1 day = 3 : 2
[ Bs work doen = x (let), then As work done = $$\frac{x+50}{100}$$x =$$\frac{3}{2}$$x So, (A : B)s work done =$$\frac{3}{2}$$x:x or 3 : 2 ]
Work done by A and B together in 1 day =$$\frac{1}{15}$$
As 1 days work =$$\frac{1}{15}$$*$$\frac{3}{5}$$ =$$\frac{1}{25}$$
Hence, A alone will finish the work in 25 days.

Ans .

(2)18 days

1. Explanation :

(2) Using Rule 2,
If Tapas alone takes x days to complete the work, then $$\frac{1}{x}$$ +$$\frac{1}{2x}$$ =$$\frac{1}{12}$$
=> $$\frac{2+1}{2x}$$ =$$\frac{1}{12}$$
=>2x = 36 => x = 18 days.

Ans .

(3) 20 days

1. Explanation :

(3) (A + B)s 1 days work = $$\frac{1}{12}$$....... (i)
(B + C)s 1 days work =$$\frac{1}{15}$$.......... (ii)
Difference between A and Cs 1 days work =$$\frac{1}{12}$$-$$\frac{1}{15}$$=$$\frac{5-4}{60}$$=$$\frac{1}{60}$$
If A alone completes the work in x days, C will do the same in 2x days.
$$\frac{1}{x}$$-$$\frac{1}{2x}$$=$$\frac{1}{60}$$
=> $$\frac{2-1}{x}$$ =$$\frac{1}{60}$$=>$$\frac{1}{2x}$$=$$\frac{1}{60}$$
=> x = 30
Bs 1 days work = $$\frac{1}{12}$$-$$\frac{1}{30}$$ [From equation (i)]
$$\frac{5-2}{60}$$ =$$\frac{3}{60}$$ =$$\frac{1}{20}$$
Hence, B alone will complete the work in 20 days

Ans .

(2) 6$$\frac{2}{3}$$ days

1. Explanation :

(2) If B alone completes the work in x days, A will do the same in 2x days.
(A + B)s 1 days work
$$\frac{1}{x}$$+$$\frac{1}{2x}$$=$$\frac{2+1}{2x}$$=$$\frac{3}{2x}$$and Cs 1 days work =$$\frac{3}{4x}$$
$$\frac{3}{4x}$$=$$\frac{1}{20}$$
=>4x = 3 * 20
=> x =$$\frac{3*20}{4}$$ =15
(A + B + C)s 1days work =$$\frac{1}{2x}$$+$$\frac{1}{x}$$+$$\frac{3}{4x}$$=$$\frac{1}{30}$$+$$\frac{1}{15}$$+$$\frac{1}{20}$$
. $$\frac{2+4+3}{60}$$=$$\frac{9}{60}$$=$$\frac{3}{20}$$
Hence, all three together will complete the work in$$\frac{20}{3}$$ or 6$$\frac{2}{3}$$days.

Ans .

(2)22$$\frac{1}{2}$$ days

1. Explanation :

(2) Using Rule 2,
If A completes the work in x days, B will do the same in 3x days.
=>3x - x = 60
=> 2x = 60
=> x = 30 and 3x = 90
(A + B)s 1 days work =$$\frac{1}{30}$$+$$\frac{1}{90}$$=$$\frac{3+1}{90}$$=$$\frac{4}{90}$$=$$\frac{2}{45}$$
A and B together will do the work in$$\frac{45} {2}$$ or 22$$\frac{1}{2}$$ days

Ans .

(2) 6 hours

1. Explanation :

(2) A does 20% less work than B.
Ratio of time taken = 5 : 4
A completes a work in $$\frac{15}{2}$$ hours
Time taken by B to do the same work =$$\frac{15}{2}$$*$$\frac{4}{5}$$= 6 hours.

Ans .

(3) 10 days

1. Explanation :

(3) Using Rule 15,
Efficiency and time taken are inversely proportional Bimal : Kamal = 150 : 100 (work)
=> 100 : 150 (Time) = 2 : 3
=> 3 units => 15 days
=> 2 units => $$\frac{15}{3}$$*2=10 days.

Ans .

(3) 6 days

1. Explanation :

(3) Let time taken by C to complete the work = x days
Time taken by A to complete the work = 3x days and time taken by B to complete the work = $$\frac{3x}{2}$$days
According to the question,

$$\frac{1}{3x}$$+$$\frac{2}{3x}$$+$$\frac{1}{x}$$=1
=>$$\frac{1+2+3}{3x}$$ =1
=>$$\frac{6}{3x}$$ =1
=>$$\frac{2}{x}$$ =1
=>x = 2
Time taken by A= 3x = 3 * 2 = 6 days

Ans .

(4) 15 days

1. Explanation :

(4) Using Rule 2,
Time taken by A to complete the work = x days
Time taken by B to complete the work = 3x days
So, 3x - x = 2x = 40
=> x = 20 and 3x = 60
=> (A + B)s 1 days work= $$\frac{1}{20}$$+$$\frac{1}{60}$$=$$\frac{3+1}{60}$$=$$\frac{4}{60}$$=$$\frac{1}{15}$$
A and B together will completethe work in 15 days.

Ans .

(2) 21 days

1. Explanation :

(2) Using Rule 2,
If A completes the work in x days, B will take 2x days.
$$\frac{1}{x}$$+$$\frac{1}{2x}$$=$$\frac{1}{14}$$=>$$\frac{2+1}{2x}$$=$$\frac{1}{14}$$
=> 2x = 42 => x = 21 day

Ans .

(3) 15 days

1. Explanation :

(3) Time taken by B
$$\frac{21*100}{140}$$=15 days.

Ans .

(3) 25

1. Explanation :

(3) Using Rule 2,
If the time taken by B to complete the work be x days, then time taken by A = (x-5) days.
$$\frac{1}{x}$$+$$\frac{1}{x-5}$$=$$\frac{9}{100}$$
=>$$\frac{x-5+x}{x(x-5)}$$ =$$\frac{9}{100}$$
=>9x2- 45x =200x -500
=>9x2-245x + 500 = 0
=>9x2-225x-20x + 500 = 0
=>9x(x-25)-20 (x-25) = 0
=>(x-25) (9x-20) = 0
=>x = 25 because x !=$$\frac{20}{9}$$

Ans .

(1) 30 days

1. Explanation :

(1) Using Rule 2,
Let time taken by B in completing the work = x days
Time taken by A = (x-10) days
$$\frac{1}{x}$$+$$\frac{1}{x-10}$$=$$\frac{1}{12}$$
$$\frac{x-10+x}{x(x-10)}$$=$$\frac{1}{12}$$
=>24x-120 =x2- 10x
=>x2-34x + 120 = 0
=>x2-30x-4x+120 = 0
=>x(x-30)-4(x-30) = 0 =>(x-4) (x-30) = 0 =>x = 30 because x is not equal to 4.

Ans .

(3) 6 days

1. Explanation :

(3) Time taken by B=9*$$\frac{100}{150}$$= 6 days.

Ans .

(2)13 days

1. Explanation :

(2) Using Rule 2,
Time taken by B=$$\frac{130}{100}$$*23=$$\frac{299}{10}$$days
(A + B)s 1 days work=$$\frac{1}{23}$$+$$\frac{10}{299}$$=$$\frac{13+10}{299}$$=$$\frac{23}{299}$$=$$\frac{1}{13}$$
Time taken by (A + B) = 13 days.

Ans .

(2) 2 : 1

1. Explanation :

5m + 2w = 4m + 4w
=>m = 2w
=> Required ratio = 2 : 1

Ans .

(1)7$$\frac{1}{2}$$ days

1. Explanation :

(1) Time taken by B =12*$$\frac{100}{160}$$
=$$\frac{15}{2}$$=7$$\frac{1}{2}$$ days

Ans .

(4)$$\frac{60}{13}$$ days

1. Explanation :

(4) Time taken by B in completing the work
=12*$$\frac{100}{160}$$=$$\frac{15}{2}$$ days.
(A+B)s 1 days work =$$\frac{1}{12}$$+$$\frac{2}{15}$$ =$$\frac{5+8}{60}$$ =$$\frac{13}{60}$$
Hence, the work will be completed in $$\frac{60}{13}$$ days.

Ans .

(3)36 days

1. Explanation :

(3) Using Rule 2,
If A alone completes the work in x days, B will complete the same in 2x days.
=$$\frac{1}{x}$$+$$\frac{1}{2x}$$=$$\frac{1}{12}$$
=>$$\frac{2+1}{2x}$$ = $$\frac{1}{12}$$
=>2x = 36
=>B alone will complete the work in 36 days (i.e. 2x ).

Ans .

(1)18 days

1. Explanation :

(1) Using Rule 2,
Let time taken by P = x days Then, time taken by Q = 3x days
=> 3x - x = 48 => x = 24 => (P + Q)s 1 days work =$$\frac{1}{24}$$+$$\frac{1}{72}$$=$$\frac{3+1}{72}$$=$$\frac{1}{18}$$
Required time = 18 days.

Ans .

(2)24 days

1. Explanation :

(2) Using Rule 2 and 3,
If B does the work in 3x days, (A + C) will do the same work in x days.
If C does that work in 2y days.(A + B) will do it in y days.
$$\frac{1}{x}$$+$$\frac{1}{3x}$$=$$\frac{1}{10}$$
=>$$\frac{4}{3x}$$=$$\frac{1}{10}$$
=>3x = 40
=>x=$$\frac{4}{5}$$
Again,$$\frac{1}{y}$$+ $$\frac{1}{2y}$$=$$\frac{1}{10}$$
=> $$\frac{3}{2y}$$=$$\frac{1}{10}$$ => y=15
(A + B + C)s 1 days work =$$\frac{1}{10}$$
=>$$\frac{1}{A}$$+$$\frac{1}{40}$$+$$\frac{1}{30}$$=$$\frac{1}{10}$$
=>$$\frac{1}{A}$$= $$\frac{1}{10}$$-$$\frac{1}{40}$$-$$\frac{1}{30}$$
=$$\frac{12-3-4}{120}$$=$$\frac{1}{24}$$
A alone will complete the work in 24 days

Ans .

(1)4$$\frac{4}{5}$$days

1. Explanation :

(1) Ratio of A's and B's efficiency = 4 : 5
Ratio of time taken = 5 : 4
Time taken by B =$$\frac{6*4}{5}$$ =$$\frac{24}{5}$$=4$$\frac{4}{5}$$days.

Ans .

(2)6$$\frac{1}{4}$$ days

1. Explanation :

(2) Using Rule 2,
If A alone does the work in x days and B alone does the work in y days, then
$$\frac{1}{x}$$+$$\frac{1}{y}$$=$$\frac{1}{5}$$.....(i)
Again,$$\frac{2}{x}$$+$$\frac{1}{3y}$$=$$\frac{1}{3}$$ ....(ii)
By equation (ii) * 3 - (i)
$$\frac{6}{x}$$+$$\frac{1}{y}$$-$$\frac{1}{x}$$-$$\frac{1}{y}$$=1- $$\frac{1}{5}$$
=>$$\frac{6}{x}$$-$$\frac{1}{x}$$=$$\frac{4}{5}$$
=>$$\frac{6-1}{x}$$=$$\frac{4}{5}$$
=> x= $$\frac{25}{4}$$ =6$$\frac{1}{4}$$ days.

Ans .

(4)1$$\frac{5}{19}$$ days

1. Explanation :

(4) Using Rule 3,
Time taken by Ramesh
= 4*$$\frac{2}{3}$$=$$\frac{8}{3}$$days.
Work done by all three in 1 day
$$\frac{1}{4}$$+$$\frac{1}{6}$$+$$\frac{3}{8}$$=$$\frac{6+4+9}{24}$$=$$\frac{19}{24}$$
Required time =$$\frac{24}{19}$$=1$$\frac{5}{19}$$ days.

Ans .

(3)30 days, 90 days

1. Explanation :

(3) Time taken by Sonia = 3x days (let)
=>Time taken by Pratibha = x days
=>3x - x = 60 => 2x = 60
=>x = 30 days
=>Time taken by Sonia = 3x days = 3 * 30 = 90 days.

Ans .

(1)33 days

1. Explanation :

(1) Using Rule 3,
Let time taken by A = x days
Time taken by B = 2x days
Time taken by C = 3x days
According to the question,
$$\frac{1}{x}$$+$$\frac{1}{2x}$$+$$\frac{1}{3x}$$=$$\frac{1}{6}$$
=>$$\frac{6+3+2}{6x}$$=$$\frac{1}{6}$$
=>$$\frac{11}{6x}$$$$\frac{1}{6}$$
=>6x = 6 * 11
=> x=$$\frac{6*11}{6}$$=11
=>Time taken by C alone = 3x= 3 * 11 = 33 days.

Ans .

(4)24 days

1. Explanation :

(4) A is twice as good as B.
Time taken by A = x days
Time taken by B = 2x days
According to the question,
$$\frac{1}{x}$$+$$\frac{1}{2x}$$=$$\frac{1}{16}$$
=>$$\frac{2+1}{2x}$$ =$$\frac{1}{16}$$
=> $$\frac{3}{x}$$=$$\frac{1}{8}$$
=> x = 3 * 8 = 24 days.

Ans .

(2) 16

1. Explanation :

(2) According to the question,
1 man = 2 boys
3 men + 4 boys
=(3 + 2) men = 5 men
= M1D1= M2D2
=> 5 * D1 = 10 * 8
=>D11= $$\frac{10*8}{5}$$ = 16 days.

Ans .

(1)4

1. Explanation :

(1) A is twice efficient than B.
Time taken by B = 12 days
=>Time taken by A = 6 days
(A + B)s 1 days work =$$\frac{1}{6}$$+$$\frac{1}{12}$$=$$\frac{2+1}{12}$$=$$\frac{1}{4}$$
Required time = 4 days.

Ans .

(1)5 days

1. Explanation :

(1) In second case, the efficiency of a man is twice to that in the first case
=>M1D1= 2M2D2
=>10 * 20 = 2 * 20 * D2
D2 =$$\frac{10*20}{2*20}$$ =5 days.

Ans .

(2)16

1. Explanation :

(2) Time taken by Shashi in doing 1 work = 20 days
Tanya is 25% more efficient than Shashi.
Time taken by Tanya =$$\frac{100}{125}$$ * 20= 16 days.

# TYPE-VI

Ans .

(2)13 days

1. Explanation :

Ans .

(1)30

1. Explanation :

Ans .

(1)15

1. Explanation :

(1) Using Rule 1,
7 men = 10 women
or 1 man =$$\frac{10}{7}$$women
14 men + 20 women
($$\frac{10*14}{7}$$+20) women = 40 women
Now, more work, more days More women, less days
Work 1:6 women 40:10 } ::10:x
Where x = number of days
=> 1 * 40 * x = 6 * 10 * 10 or x = $$\frac{600}{40}$$=15

Ans .

(1)10 hours

1. Explanation :

Ans .

(4)16

1. Explanation :

x=$$\frac{8*8*4}{4*4}$$=16.

Ans .

(1) 6 days

1. Explanation :

Ans .

(1)3

1. Explanation :

Ans .

(4) n3/p2

1. Explanation :

4)P men working P hours/ day for P days produce P units of work.
1 man working 1 hour/day for 1 day produce
= p/p3 = 1/p2 units of work
n men working n hours a da for n days produce n3/p2units of work

Ans .

(2)10 days

1. Explanation :

Ans .

(3)14

1. Explanation :

Ans .

(3)12

1. Explanation :

Ans .

(2)20

1. Explanation :

(2) Using Rule 1,
Let the original number of carpenters be x.
=>M1D1=M2D2
=>x * 9 = (x-5) * 12
=>9x = 12x-60
=>3x = 60 => x = 20

Ans .

(2)16 days

1. Explanation :

(2) Using Rule 1,
=>2 men + 3 women = 4 men => 2 men = 3 women \ 3 men + 3 women = 5 men =>M1D1=M2D2
=> 4 * 20 = 5 *D2
=>D2=$$\frac{4*20}{5}$$ =16 days.

Ans .

(1)12 hours

1. Explanation :

Ans .

(4)3 days

1. Explanation :

Ans .

(4)8

1. Explanation :

=> $$\frac{9}{10}$$=$$\frac{(x-1)(x+1)}{(x+2)(x-1))}$$=$$\frac{x+1}{x+2}$$
=>10x + 10 = 9x + 18
=> x = 18-10 = 8

Ans .

(3)8 hrs.

1. Explanation :

(3) Using Rule 1,
=>M1D1T1=M2D2T2
=>80*16*6 = 64*15*T2
=>T2 =$$\frac{80*16*6}{64*15}$$=8 hours.

Ans .

(1)16 days

1. Explanation :

(1) Using Rule 1,
=>M1D1=M2D2
=>18 * 24 = 27 * D2
D2=$$\frac{18*24}{27}$$= 16 days.

Ans .

(3)43$$\frac{7}{11}$$ hours

1. Explanation :

Ans .

(3)x2/y days

1. Explanation :

(3) Using Rule 1,
=>M1D1= M2D2
=> x.x = y.D2
=>D2= x2/y days.

Ans .

(2)15 days

1. Explanation :

Using Rule 1,
=>M1D1= M2D2
=> 30 * 18 = 36 * D2
=>D2= $$\frac{30*18}{36}$$ = 15 days.

Ans .

(1)10 days

1. Explanation :

1) 20 men = 24 women
=> 5 men = 6 women
=> 30 men + 12 women
= 40 men
=>M1D1= M2D2
=> 20 * 20 = 40 * D2
D2=$$\frac{20*20}{40}$$= 10 days.

Ans .

(3)34 days

1. Explanation :

Ans .

(4)20 days

1. Explanation :

(4) 3 * 5 men + 7 * 5 women
= 4 * 4 men + 6 * 4 women
=> 16 men - 15 men = 35 women - 24 women
=>1 man = 11 women
=> 3 men + 7 women = 40 women
=>M1D1= M2D2
=> 40 * 5 = 10 * D2
=>D2 = 20 days.

Ans .

(4)30

1. Explanation :

Ans .

(2)100

1. Explanation :

(2) Using Rule 1,
200 men do $$\frac{1}{4}$$ work in 50 days.

Ans .

(2)56

1. Explanation :

Ans .

(2)$$\frac{125}{49}$$

1. Explanation :

Ans .

(1)300

1. Explanation :

(1) Using Rule 1,
=>M1D1 =M2D2
=>75 * 90 = M2*18
=>M2=$$\frac{75*90}{18}$$=375
=> Number of additional men = 375-75 = 300.

Ans .

(3)5 days

1. Explanation :

(*) 4 men = 8 women
=> 1 man = 2 women
=> 6 men + 12 women
=> 12 women + 12 women = 24 women
=>M1D1 =M2D2
=> 8 * 15 = 24 * D2
=>D2 =$$\frac{8*15}{24}$$= 5days.

Ans .

(1)8

1. Explanation :

=>M1D1 =M2D2
=>24 * 17 = M2*51
=>M2 =$$\frac{24*17}{51}$$ =8 men.

# TYPE-VII

Ans .

(2)₹60

1. Explanation :

2) Ratio of Sumans and Sumatis 1 days work = $$\frac{1}{3}$$:$$\frac{1}{2}$$ =2:3
Sum of the ratios = 2 + 3 = 5
Sumans share =$$\frac{2}{5}$$*150=₹60.

Ans .

(2)₹200.20

1. Explanation :

(2) Total wages of 500 workers = 500 × 200 = 100000
Now, according to question,
Correct Average =$$\frac{100000-180-20+80+220}{500}$$
=> $$\frac{100100}{500}$$ =₹200.20.

Ans .

(3)₹750

1. Explanation :

(3) Using Rule 25,
Cs 1 days work =$$\frac{1}{4}$$-($$\frac{1}{8}$$+$$\frac{1}{12}$$)=$$\frac{1}{4}$$-($$\frac{3+2}{24}$$)
=>$$\frac{1}{4}$$-$$\frac{5}{24}$$=$$\frac{6-5}{24}$$=$$\frac{1}{24}$$
=>A : B : C =$$\frac{1}{8}$$:$$\frac{1}{12}$$:$$\frac{1}{24}$$=3:2:1
=> C's share =₹($$\frac{1}{6}$$*4500)=₹750.

Ans .

(3)₹9450

1. Explanation :

Ans .

(2)₹400

1. Explanation :

(2) Using Rule 25,
As 1 days work =$$\frac{1}{6}$$
Bs 1 days work =$$\frac{1}{8}$$ and (A + B + C)s 1 days work =$$\frac{1}{3}$$
Cs 1days work =$$\frac{1}{3}$$-$$\frac{1}{6}$$-$$\frac{1}{8}$$=$$\frac{8-4-3}{24}$$=$$\frac{1}{24}$$
Ratio of their one day’s work respectively=$$\frac{1}{6}$$:$$\frac{1}{8}$$:$$\frac{1}{24}$$=4:3:1
Sum of the ratios = 4 + 3 + 1 = 8
=> Cs share =$$\frac{1}{8}$$*3200=₹400.

Ans .

(4)₹12,000

1. Explanation :

(4) As 1 days work =$$\frac{1}{15}$$
Bs 1 days work =$$\frac{1}{10}$$
Ratio =$$\frac{1}{15}$$:$$\frac{1}{10}$$=2:3
Sum of the ratios = 2 + 3 = 5
As share =₹($$\frac{2}{5}$$*300000) =₹12,000.

Ans .

(4)₹40

1. Explanation :

(4) Man : boy = 3 : 1
Boys share = $$\frac{1}{4}$$*800 = 200.
The daily wages of boy=₹($$\frac{200}{5}$$)=₹40.

Ans .

(2)₹250

1. Explanation :

Ans .

(2)₹600

1. Explanation :

(2) Using Rule 25,
Ratio of wages of A, B and C respectively
= 5 * 6 : 6 * 4 : 4 * 9
= 30 : 24 : 36 = 5 : 4 : 6
Amount received by A =$$\frac{5}{5+4+6}$$*1800
=$$\frac{5}{15}$$*1800=₹600.

Ans .

(3)4

1. Explanation :

(3) Total salary for 20 days= (75 × 20) = 1500
Difference = (1500 – 1140) = 360
Money deducted for 1 day’s absencefrom work= (15 + 75) = 90
Number of days he was absent =$$\frac{360}{90}$$=4 days.

Ans .

(3)₹275

1. Explanation :

(3) Using Rule 25,
First mans 1 days work =$$\frac{1}{7}$$
Second mans 1 days work =$$\frac{1}{8}$$
Let, Boys 1 days work =$$\frac{1}{x}$$
=>$$\frac{1}{7}$$+$$\frac{1}{8}$$+$$\frac{1}{x}$$=$$\frac{1}{3}$$
=>$$\frac{1}{x}$$ = $$\frac{1}{3}$$-$$\frac{1}{7}$$-$$\frac{1}{8}$$
=>$$\frac{56-24-21}{168}$$=$$\frac{11}{168}$$
=> Ratio of their one days work=$$\frac{1}{7}$$:$$\frac{1}{8}$$:$$\frac{11}{168}$$=24:21:11
=>Sum of the ratios = 24 + 21 + 11= 56
=> Boys share in wages =$$\frac{11}{56}$$*1400 =₹275.

Ans .

(4)₹17,100

1. Explanation :

(4) 5 men = 7 women
[Both earn same amount in 1 day]
7 men =$$\frac{7}{5}$$*7 =$$\frac{49}{5}$$ women
7 men + 13 women
=>$$\frac{49}{5}$$+13 =$$\frac{114}{5}$$ women
Now,7 women = 5250 => $$\frac{114}{5}$$ women
=>$$\frac{5250}{7}$$*$$\frac{114}{5}$$=₹17,100.

Ans .

(1)₹400

1. Explanation :

(1) According to the question,
(2 × 14) men + 14 women
= 16 men + 32 women
=>(28 – 16) men =(32–14) women
=> 12 men = 18 women
=> 2 men = 3 women
1 woman =$$\frac{2}{3}$$man
Amount received by 1 woman per day= $$\frac{2}{3}$$*600=₹400.

Ans .

(3)₹160

1. Explanation :

(3) Using Rule 25,
Work done by the third person in 1 day=$$\frac{1}{8}$$-$$\frac{1}{16}$$-$$\frac{1}{24}$$=$$\frac{6-3-2}{48}$$=$$\frac{1}{48}$$
Ratio of their 1 day’s work=$$\frac{1}{16}$$:$$\frac{1}{24}$$:$$\frac{1}{48}$$=3:2:1
Share of the third person =$$\frac{1}{3+2+1}$$*960=$$\frac{960}{6}$$
=>₹160.

Ans .

(1)6:5

1. Explanation :

(1) Using Rule 25,
Required ratio = 15 * 22 : 11 * 25 = 6 : 5

Ans .

(4)₹12000

1. Explanation :

(4) Experts 1 days work=$$\frac{1}{12}$$-$$\frac{1}{36}$$-$$\frac{1}{48}$$
=>$$\frac{12-4-3}{144}$$=$$\frac{5}{144}$$
Ratio of their respective work for 1 day =$$\frac{1}{36}$$:$$\frac{1}{48}$$:$$\frac{5}{144}$$=4:3:5
Experts share =$$\frac{5}{12}$$*28800=₹12000.

Ans .

(1)₹300

1. Explanation :

(1) Using Rule 25,
According to the question
$$\frac{1}{15}$$ +$$\frac{1}{12}$$ +$$\frac{1}{C}$$ =$$\frac{1}{5}$$
Let C1s work in day be $$\frac{1}{C}$$
$$\frac{1}{C}$$=$$\frac{1}{5}$$-$$\frac{1}{15}$$-$$\frac{1}{12}$$=$$\frac{12-4-5}{60}$$=$$\frac{1}{20}$$
=>A:B:C=$$\frac{1}{15}$$:$$\frac{1}{12}$$:$$\frac{1}{20}$$=4:5:3
=> Cs share =$$\frac{3}{12}$$*1200 = ₹300.

Ans .

(4)12 days

1. Explanation :

(4) As 1 days work = $$\frac{1}{21}$$
Bs 1 days work = $$\frac{1}{28}$$
Total work done by both=$$\frac{1}{21}$$+$$\frac{1}{28}$$=$$\frac{4+3}{84}$$=$$\frac{1}{12}$$
Amount is sufficient to pay 12 days wages of both.

Ans .

(4)₹400

1. Explanation :

(4) Rule 2 and Rule 25,
Work done by A and B in 5 days = 5($$\frac{1}{12}$$+$$\frac{1}{15}$$)
=5($$\frac{5+4}{60}$$)=$$\frac{9}{12}$$=$$\frac{3}{4}$$
Time taken by C in doing $$\frac{1}{4}$$work = 5 days
C will complete in 20 days.
Ratio of wages = $$\frac{1}{12}$$:$$\frac{1}{15}$$:$$\frac{1}{20}$$
=>5:4:3
Amount received by A= $$\frac{5}{12}$$*960 = ₹400

Ans .

(2)₹20

1. Explanation :

(2) The daily earning of 'C' = Daily earning of (A + C) and (B + C) - Daily earning of (A + B + C) = 94 + 76 - 150 = 20

Ans .

(3)₹225

1. Explanation :

(3) Rule 3 and Rule 25,
If the fourth person completes the work in x days, then
$$\frac{3}{8}$$+$$\frac{3}{12}$$+$$\frac{3}{16}$$+$$\frac{3}{x}$$=1
=>$$\frac{1}{x}$$ = $$\frac{1}{3}$$-$$\frac{1}{8}$$-$$\frac{1}{12}$$-$$\frac{1}{16}$$
=>$$\frac{16-6-4-3}{48}$$ =>$$\frac{1}{16}$$
x = 16
Ratio of wages =$$\frac{1}{8}$$:$$\frac{1}{12}$$:$$\frac{1}{16}$$:$$\frac{1}{16}$$=6:4:3:3
Sum of ratios = 6 + 4 + 3+3 = 16
Fourth persons share =$$\frac{3}{16}$$*1200=₹225.

Ans .

(1) A : 150, B : 100, C : 150

1. Explanation :

(1) Rule 3 and Rule 25,
If C alone completes the work in x days, then
$$\frac{1}{16}$$+$$\frac{1}{24}$$+$$\frac{1}{x}$$=$$\frac{1}{6}$$
=> $$\frac{1}{x}$$ = $$\frac{1}{6}$$-$$\frac{1}{16}$$-$$\frac{1}{24}$$
=>$$\frac{8-3-2}{48}$$=$$\frac{1}{16}$$
=>x = 16 days
Ratio of their remuneration =$$\frac{1}{16}$$:$$\frac{1}{24}$$:$$\frac{1}{16}$$= 3:2:2
As remuneration =$$\frac{3}{8}$$*400 = ₹150
Bs remuneration =$$\frac{2}{8}$$*400 =₹100
Cs remuneration =$$\frac{3}{8}$$*400 =₹150
=> A : 150, B : 100, C : 150

Ans .

(4)143.50

1. Explanation :

(4) Using Rule 25,
Skilled : half skilled : unskilled =$$\frac{1}{3}$$:$$\frac{1}{4}$$:$$\frac{1}{6}$$
=>($$\frac{1}{3}$$*12) :($$\frac{1}{4}$$*12):($$\frac{1}{6}$$*12)
= 4 : 3 : 2 Share of the trained labourer =$$\frac{28}{(7*4+8*3+2*10)}$$ *369 =$$\frac{28}{28+24+20}$$*369
=>$$\frac{28}{72}$$*369 =143.50.

Ans .

(2)₹100

1. Explanation :

(2) Work done by B= 1-$$\frac{19}{23}$$ = $$\frac{23-19}{23}$$ = $$\frac{4}{23}$$
(A + C) : B = $$\frac{19}{23}$$:$$\frac{4}{23}$$ =19:4
Sum of ratios = 19 + 4 = 23
Bs share =$$\frac{4}{23}$$*575 =₹100

Ans .

(4)5 hours

1. Explanation :

Rate of earning of the man = 2000/50 = Rs. 40 per hour
Rate of earning for additional hours = 40 × 3/2 = Rs. 60 per hour
Let the man has to work for n additional hours.
Then, 2000 + n × 60 = 2300
⇒ n × 60 = 300
⇒ n = 5h.

Ans .

(3)Rs.120

1. Explanation :

(3) (2 men + 1 woman)s 14 days work = (4 women + 2 men)s 8 days work
=> 28 men + 14 women
=> 32 women + 16 men
=> (28 - 16) = 12 men
=> (32 - 14) = 18 women
=> 2 men = 3 women
1 woman = $$\frac{2}{3}$$ man
=> Wages per day of 1 man = Rs. 180
=> Wages per day of 1 woman$$\frac{2}{3}$$*180 =Rs.120.

Ans .

(1)Rs. 67.50

1. Explanation :

(1) Time taken by A =$$\frac{63}{3.50}$$= 18 days
Time taken by B =$$\frac{75}{2.5}$$ =30 days.
(A + B)s 1 days work =$$\frac{1}{18}$$+$$\frac{1}{30}$$ = $$\frac{5+3}{90}$$ =$$\frac{8}{90}$$ = $$\frac{4}{45}$$
Required time =$$\frac{45}{4}$$ days
Total wages =$$\frac{45}{4}$$ * (3.50 + 2.50)
=>Rs($$\frac{45}{4}$$*6) = )Rs. 67.5.

Ans .

(3) Rs.250

1. Explanation :

(3) Ratio of As and Bs 1 days work =$$\frac{1}{12}$$:$$\frac{1}{15}$$ = 15:12 => 5:4
Sum of the terms of ratio = 5 + 4 = 9
As share = Rs.($$\frac{5}{9}$$*450) = Rs.250.

Ans .

(1)Rs. 200

1. Explanation :

(1) Part of work done by C
=> 1- $$\frac{7}{11}$$-$$\frac{4}{11}$$
=> Total amount received = Rs. 550
=> Cs share = Rs($$\frac{4}{11}$$*550) =Rs. 200.

Ans .

(1)Rs.50

1. Explanation :

(1) Let C alone complete the work in x days.
According to the question,
$$\frac{1}{5}$$+$$\frac{1}{15}$$+$$\frac{1}{x}$$=$$\frac{1}{3}$$
=>$$\frac{1}{x}$$ =$$\frac{1}{3}$$-$$\frac{1}{5}$$-$$\frac{1}{15}$$
=>$$\frac{5-3-1}{15}$$ =>$$\frac{1}{15}$$
\ => x = 15 days = Time taken by C alone.
Ratio of the 1 day’s work of A, B and C =$$\frac{1}{5}$$:$$\frac{1}{15}$$:$$\frac{1}{15}$$ => 3:1:1
Sum of the terms of ratio = 3 + 1 + 1 = 5
C’s share = Rs($$\frac{1}{5}$$*250) => Rs.50

Ans .

(1) Man ₹2.75, Woman ₹2.25

1. Explanation :

(1) Let daily wages of a man be Rs. x
Daily wages of a woman = Rs.(x-$$\frac{1}{2}$$)
According to the question, 600x + 400(x-$$\frac{1}{2}$$)
= 1000 × 2.55
=> 600x + 400x - 200 = 2550
=> 1000x = 2550 + 200 = 2750
=> x=$$\frac{2750}{1000}$$ =Rs. 2.75
=> Daily wages of a woman
=>Rs. (2.75 – 0.5)
=>Rs. 2.25

# TYPE-VIII

Ans .

(1) 10

1. Explanation :

(1) Let initially the number of men
be x.
=> According to question,
M1D1W2 = M2D2W1
x*30 = (x + 5)*(30 - 10)
x*30 = 20x + 100
30x - 20x = 100
10x = 100
x = 10

Ans .

(4) 8

1. Explanation :

(4) Using Rule 1,

=> 450*10*5*x
= 625*8*6*6
=> x = $$\frac{625*8*6*6}{450*10*5}$$ = 8

Ans .

(1) 24 days

1. Explanation :

(1) Work done by A in 15 days
= $$\frac{1}{60}$$*15 = $$\frac{1}{4}$$
Remaining work = 1-$$\frac{1}{4}$$ = $$\frac{3}{4}$$
Now, $$\frac{3}{4}$$ work is done by B in 30
days
Whole work will be done by B in
$$\frac{30*4}{3}$$ = 40 days
As 1 days work = $$\frac{1}{60}$$ and Bs 1
days work = $$\frac{1}{40}$$
(A + B)s 1 days work
= $$\frac{1}{60}$$+$$\frac{1}{40}$$ = $$\frac{2+3}{120}$$ = $$\frac{5}{120}$$ = $$\frac{1}{24}$$
Hence, both will finish the work in 24 days.

Ans .

(2) 25 days

1. Explanation :

(2) As 1 days work
= (B +C)s 1 days work ...(i)
(A + B)s 1 days work = $$\frac{1}{10}$$
Cs 1 days work = $$\frac{1}{50}$$
(A + B + C)s 1 days work
= $$\frac{1}{10}$$+$$\frac{1}{50}$$ = $$\frac{5+1}{50}$$ = $$\frac{6}{50}$$ = $$\frac{3}{25}$$ ...(iii)
(A + A)s 1 days work = $$\frac{3}{25}$$
(By (i) & (iii)
As 1 days work = $$\frac{3}{50}$$
Bs 1 days work = $$\frac{1}{10}$$-$$\frac{3}{50}$$
= $$\frac{5-3}{50}$$ = $$\frac{2}{50}$$ = $$\frac{1}{25}$$
Hence, B alone will complete the
work in 25 days

Ans .

(3) 7$$\frac{1}{2}$$ days

1. Explanation :

(3) Using Rule 2,
Let the son take x days to do the
work.
$$\frac{1}{5}$$+$$\frac{1}{x}$$ = $$\frac{1}{3}$$
=> $$\frac{x+5}{5x}$$ = $$\frac{1}{2}$$
=> 3x + 15 = 5x
=> 2x = 15 => x = $$\frac{15}{2}$$ = 7$$\frac{1}{2}$$ days

Ans .

(4) 40

1. Explanation :

(4) Let the number of men in the
beginning = x
Then, $$\frac{x+8}{x}$$ = $$\frac{60}{50}$$
=> $$\frac{x+8}{x}$$ = $$\frac{6}{5}$$
=> 6x = 5x + 40 => x = 40

Ans .

(1) 192

1. Explanation :

(1) 12 persons can complete a
work in 4 days.
=> 24 persons can complete the work in 2 days.
=> 24 persons can complete the 8 times work in 16 days
=> 24*8 persons = 192 persons can complete the 8 times work in 2 days.

Ans .

(2) 110

1. Explanation :

(2) Let the original number of
workers = x. Then,
x*100 = (x -10)*110
=> 10x = 11x - 110
=> x = 110

Ans .

(3) 12 days

1. Explanation :

(3) Work done by 12 men in 6
days = $$\frac{1}{2}$$
Remaining work
= 1-$$\frac{1}{2}$$ = $$\frac{1}{2}$$
6 men leave the work.
Time taken = $$\frac{12*12}{6*2}$$ = 12 days

Ans .

(2) 15

1. Explanation :

(2) Using Rule 1,
60 men can complete a work in
250 days.
Work done by 60 men in 1 day
= $$\frac{1}{250}$$
=> Work done by 60 men in 200
days = $$\frac{200}{250}$$ = $$\frac{4}{5}$$
Remaining work = 1-$$\frac{4}{5}$$ = $$\frac{1}{5}$$
Work is stopped for 10 days.

Ans .

(1) 3 days

1. Explanation :

(1) Using Rule 2,
Working 5 hours a day, A can complete a work in 8 days.
i.e. A can complete the work in 40 hours.
Similarly, B will complete the same work in 60 hours.
(A + B)s 1 hours work
= $$\frac{1}{40}$$+$$\frac{1}{60}$$ = $$\frac{3+2}{120}$$
= $$\frac{5}{120}$$ = $$\frac{1}{24}$$
Hence, A and B together will complete the work in 24 hours.
They can complete the work in 3 days working 8 hours a day.

Ans .

(4) 2 days

1. Explanation :

(4) According to the question,
2 persons with equal abilities can do 1 job in 1 day
Time taken by 1 man to complete 1 job = 2 days
=> Time taken by 100 persons in completing 100 jobs = 2 days

Ans .

(2) 6.30 p.m.

1. Explanation :

(2) Part of the field mowed by
Ganga and Saraswati in first 2
hours
= $$\frac{1}{8}$$+$$\frac{1}{12}$$ = $$\frac{3+2}{24}$$ = $$\frac{5}{24}$$
Part of the field mowed in first
8 hours = $$\frac{5*4}{24}$$ = $$\frac{20}{24}$$ = $$\frac{5}{6}$$
Remaining work = 1 -$$\frac{5}{6}$$ = $$\frac{1}{6}$$
Now, it is the turn of Ganga, part
of work done by Ganga in 1 hour = $$\frac{1}{8}$$
Remaining work = $$\frac{1}{6}$$-$$\frac{1}{8}$$ = $$\frac{1}{24}$$
Now, time taken by Saraswati in
completing this part of work
= $$\frac{1}{24}$$*12 = $$\frac{1}{2}$$ hour
Total time = 9*$$\frac{1}{2}$$ hour
The mowing starts at 9 am.
Hence, the mowing will be completed
at 6.30 pm.

Ans .

(3) 200

1. Explanation :

(3) Using Rule 1,
Remaining work
= 5-$$\frac{7}{2}$$ = $$\frac{3}{2}$$
M1D1W2 = M2D2W1
=> 280*80*$$\frac{3}{2}$$ = M2*20*$$\frac{7}{2}$$
=> M2 = $$\frac{280*80*30}{20*7}$$ = 480
Required number of additionalmen = 480 - 280 = 200

Ans .

(1) 6 days

1. Explanation :

(1) Let B alone do the work in x
days.
6*$$\frac{1}{12}$$ + 3*$$\frac{1}{x}$$ = 1
=> $$\frac{1}{2}$$+$$\frac{3}{x}$$ = 1
$$\frac{3}{x}$$ = $$\frac{1}{2}$$ => x = 6 days

Ans .

(4) 4:3

1. Explanation :

(4) Using Rule 15,
Efficiency and time taken are inversely
proportional.
Required ratio = 4:3

Ans .

(3) 75

1. Explanation :

(3) Scheduled time to complete the
work = 40 days
25 men in 24 days do $$\frac{1}{3}$$ work
1 man in 1 day does $$\frac{1}{3*25*24}$$ = $$\frac{1}{1800}$$ work
Work remaining = 1-$$\frac{1}{3}$$ = $$\frac{2}{3}$$
The work is to be completed 4
days before schedule i.e.,
in (40 - 4) = 36 days
No. of days left for $$\frac{2}{3}$$rd work
= 36 - 24 = 12 days
$$\frac{1}{1800}$$ work is done in 1 day by
1 man.
$$\frac{2}{3}$$rd work will be done in 12 days
by
1800*$$\frac{2}{3}$$*$$\frac{1}{12}$$ = 100 men
Extra men to be employed
= 100 - 25 = 75

Ans .

(2) 4:3

1. Explanation :

(2) 20*16 women
= 16*15 men
=> 4 women = 3 men
=> $$\frac{men}{women}$$ = $$\frac{4}{3}$$
Hence, working capacity of man :
woman = 4:3

Ans .

(1) 45 days

1. Explanation :

(1) Man : Woman (efficiency)
= 3:2
i.e., Woman completes $$\frac{2}{5}$$
th work in 18 days.
Time taken by the woman to
complete the whole work = $$\frac{18*5}{2}$$ = 45 days

Ans .

(1) 3y:2x

1. Explanation :

(1) 1 mans 1 days work = $$\frac{1}{2x}$$
1 womans 1 days work = $$\frac{1}{3y}$$
Required ratio = $$\frac{1}{2x}$$ $$\frac{1}{3y}$$
= 3y:2x

Ans .

(2) 9 hrs

1. Explanation :

(2) Using Rule 1,
D1T1 = DT2
=> 18*6 = 12*T2
=> T2 = $$\frac{18*6}{12}$$ = 9 hrs

Ans .

(3) 138

1. Explanation :

(3) Using Rule 1,

=> 12*6*240*x = 18*8*36*460
=> x = $$\frac{18*8*36*460}{12*6*240}$$ = 138

Ans .

(3) 30

1. Explanation :

(3) Using Rule 1,

=> 18*2*12*6*8x = 32*3*9*9*10*8
=> x = $$\frac{32*3*9*9*10*8}{18*2*12*6*8}$$ = 30 days

Ans .

(2) 10

1. Explanation :

(2) (P + Q)s 1 days work = $$\frac{1}{6}$$
(Q + R)s 1 days work = $$\frac{7}{60}$$
Let P alone do the work in x
days.
According to the question,
$$\frac{3}{x}$$+$$\frac{6*7}{60}$$ = 1
=> $$\frac{3}{x}$$ = 1-$$\frac{7}{10}$$ = $$\frac{3}{10}$$
=> x = 10 days
Qs 1 days work = $$\frac{1}{6}$$-$$\frac{1}{10}$$ = $$\frac{1}{15}$$
Rs 1 days work = $$\frac{7}{60}$$-$$\frac{1}{15}$$ = $$\frac{1}{20}$$
Time taken by R = 20 days
Required answer = 20 - 10
= 10 days

Ans .

(3) 25

1. Explanation :

(3) Let 150 workers complete the
work in x days.
150*x = 150 + 146 + .... to (x + 8) terms
On putting x = 17
LHS = 150*17 = 2550
RHS = 150 + 146 + .... to 25 terms
a = 150, d = - 4, n = 25
S = $$\frac{n}{2}$$*[2a+(n-1)d]
= $$\frac{25}{2}$$*[2*150 + 24*(-4)]
= $$\frac{25}{2}$$*(300-96) = 2550
Note : It is better to solve by options.

Ans .

(1) 20

1. Explanation :

(1) Using Rule 1,
According to the question,
M1D1 = M2D2
=>(x + 4)*(x + 5)
= (x - 5)*(x + 20)
=> x2 + 5x + 4x + 20
= x2 - 5x + 20x - 100
=> 9x + 20 = 15x - 100
=> 15x - 9x = 100 + 20
=> 6x = 120 => x = 20

Ans .

(3) 10 days

1. Explanation :

(3) Let the work be finished in x
days.
$$\frac{x}{50}$$+$$\frac{x-1}{50}$$+$$\frac{x-2}{50}$$+ ... + $$\frac{1}{50}$$ = 1
=> x + x - 1 + x - 2 + .... + 1 = 50
i.e., 10 + 9 + 8 + .... + 1
= 55
9 + 8 + .... + 1 = 45
Required time = 10 days

Ans .

(3) 10

1. Explanation :

(3)

=> 48*7*x = 20*21*8
=> x = $$\frac{20*21*8}{48*7}$$ => x = 10

Ans .

(2) 6$$\frac{10}{33}$$ days

1. Explanation :

(2) Area of the four walls and ceiling
of the room
= 2h (l + b) + lb
= 2*10 (25 + 12) + 25*12
= (20*37 + 300) sq. metre
= (740 + 300) sq. metre
= 1040 sq. metre
Area painted by A in 1 day
= $$\frac{250}{2}$$ = 125 sq. metre
Area painted by both in1 day
= (125 + 40) sq. metre
= 165 sq. metre
Required time = $$\frac{1040}{165}$$ = $$\frac{208}{33}$$ = 6$$\frac{10}{33}$$ days

Ans .

(1) 54

1. Explanation :

(1) Here, the length of wall is
same in both cases.
M1D1 = M2D2
=> 36*21 = M2*14
=> M2 = $$\frac{36*21}{14}$$ = 54 days

Ans .

(2) 488 kg.

1. Explanation :

(2) Number of days in April and
May = 30 + 31 = 61
Q Requirement of rice for 7 days = 56 kg.
Requirement of rice for 61 days
= $$\frac{56}{7}$$*61 = 488 kg.

Ans .

(1) 40 minutes

1. Explanation :

(1) Total working time of school
= (45*8) minutes
= 360 minutes
If 9 periods are held per day,
Working time of each period
$$\frac{360}{9}$$ = 40 minutes

Ans .

(3) 7

1. Explanation :

Ans .

(2) 45.

1. Explanation :

# TEST YOURSELF

Ans .

(2) 7$$\frac{1}{7}$$days

1. Explanation :

Ans .

(4) 8 days

1. Explanation :

Ans .

(2)120 days

1. Explanation :

(2) According to the question Work done by A and B together in one day =$$\frac{1}{10}$$ part
Work done by B and C together

Ans .

(1)42

1. Explanation :

(1) Using Rule 1,

Ans .

(2)RS.163.04

1. Explanation :

(2) Using Rule 1,
Amount received by Meeta =$$\frac{6}{23}$$*625 = Rs. 163.04

Ans .

(1)35

1. Explanation :

Ans .

(1)4 $$\frac{4}{5}$$day

1. Explanation :

(1) As one days work =$$\frac{1}{12}$$
B`s one days work =$$\frac{1}{8}$$
(A + B)s one days work=$$\frac{1}{12}$$+$$\frac{1}{8}$$ =$$\frac{2+3}{24}$$ =$$\frac{5}{24}$$
Now,$$\frac{5}{24}$$ work is done in 1day
1 work is done in = $$\frac{24}{5}$$days =4 $$\frac{4}{5}$$ days.

Ans .

(2)9 days

1. Explanation :

Ans .

(3)12 days

1. Explanation :

Ans .

(4)30 days

1. Explanation :

Ans .

(1)36 days

1. Explanation :

Ans .

(2)15 days

1. Explanation :

Ans .

(3)3$$\frac{1}{3}$$ days

1. Explanation :

Ans .

(4)9 days

1. Explanation :

Ans .

(1)40 days

1. Explanation :

Ans .

(2)24 days

1. Explanation :

Ans .

(3)18 days

1. Explanation :

Ans .

(4)15 days

1. Explanation :

Ans .

(1)20 days

1. Explanation :

Ans .

(2)16.5 days

1. Explanation :

Ans .

(3)240 days

1. Explanation :