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

# 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.