- Staff Selection Commission Mathematics 1999 to 2017 - TIME AND WORK Part 2

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

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.