# Moderate Time and Work Solved QuestionAptitude Discussion

 Q. 12 men cam complete a piece of work in 36 days, 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 day, how many women would be required?
 ✔ A. 70 ✖ B. 28 ✖ C. 66 ✖ D. 40

Solution:
Option(A) is correct

12 men in 36 days can do a work.

1 man in a day can do $\dfrac{1}{12\times 36}$work.

8 men in 20 days can do $\dfrac{8\times 20}{12\times 36}=\dfrac{10}{27}$ work.

Similarly, we find that 20 women in 20 days can do $\dfrac{10}{27}$ work.

Remaining work = $\dfrac{7}{27}$

Now, because in 60 days a work is done by 20 women.

In 1 day a work done by $20\times 60$ women.

In 4 days $\dfrac{7}{27}$ work is done by

= $\dfrac{20\times 60\times 7}{27\times 4}$  = 70 women.

## (2) Comment(s)

Harshit Varshney
()

12 men can complete a piece of work in 36 days

=> 1 man can complete the work in 36 × 12 days (∵ less man, more days. inversely proportional)

=> Work done by 1 man in 1 day =

1

36

×

12

136×12

18 women can complete the same piece of work in 60 days

=> 1 woman can complete the work in 60 × 18 days

=> Work done by 1 woman in 1 day =

1

60

×

18

160×18

Work done by 8 men and 20 women in 1 day =

8

36

×

12

+

20

60

×

18

=

1

54

+

1

54

=

1

27

836×12+2060×18=154+154=127

Work done by 8 men and 20 women in 20 days =

20

27

2027

Remaining work =

1

20

27

1−2027 =

7

27

727

Let n women complete this work in 4 days. Then

1

60

×

18

×

n

×

4

=

7

27

n

15

×

18

=

7

27

n

=

15

×

18

×

7

27

=

15

×

2

×

7

3

=

5

×

2

×

7

=

70

160×18×n×4=727n15×18=727n=15×18×727=15×2×73=5×2×7=70

Required number of women to complete the remaining work = 70

HEMANTH
()

60 days work done by 18 women .....but u have taken 20 instead of 18....