Question

18 men can complete a piece of work in 6 hours, while 30 women can complete the same work in 8 hours. 9 men start working on the job and after working for 3 hours, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 6 hours?

• A. 30
• B. 20
• C. 15
• D. None of these

Answer 1

The correct option is A

30

1 man`s 1 hour's work = $\frac{1}{18\times 6}=\frac{1}{108}$

1 woman`s 1 hour's work = $\frac{1}{30\times 8}=\frac{1}{240}$

9 men's 3 hour's work = $\frac{9}{108}\times 3=\frac{1}{4}$

Remaining work = $1-\frac{1}{4}=\frac{3}{4}$

Now, $\frac{1}{240}$ work is done in 1 hour by 1 woman

So, $\frac{3}{4}$ work will be done in 6 hours by $240\times \frac{3}{4}\times \frac{1}{6}$ = 30 women