1)

12 men can 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 days, how many women would be required ?


A) 70

B) 28

C) 66

D) 40

E) 45

Answer:

Option A

Explanation:

$12\times 36$ men can complete the work in $1$ day.

$18\times 6$ women can complete the work in $1$ day.

$12\times 36$ men $=18\times 60$ women $\Rightarrow$ 2 men = 5 women.

Now 8 men + 20 women = (4 $\times$ 5) + 20 women $=20+20$ = 40 women 18 women complete the work in 60 days.

40 women's 20 days work $= \frac{(40\times 20)}{(18\times 60)}$ $= \frac{20}{27}$

Remaining work $=\frac{7}{27}$

$18\times 60$ women do 1 work in 1 day

so that 1 woman does $=\frac{1}{(18\times 60)}$ work in 1 day

In 4 days, 1 woman does $=\frac{4}{(18\times 60)}$ $=\frac{1}{(18\times 15)}$ work

$\frac{7}{27}$ Work is done by  $\frac{(18\times 15\times 7 )}{27}$ = 70 women.