Question

Twenty four men can complete a work in sixteen days. Thirty two women can complete the same work in twenty four days. Sixteen men and sixteen women started worked for 12 days. How many more men are to be added to complete the remaining work in 2 days ?

• A. 16
• B. 24
• C. 36
• D. 48

Answer 1

The correct option is B 24

1 man's 1 days' work = $\frac{1}{24\times 16}$ $\therefore$ 16 men's 1 days' work =$\frac{16}{24\times 16}=\frac{1}{24}$ 1 woman's 1 days' work = $\frac{1}{32\times 24}$
16 women's 1 days' work = $\frac{16}{32\times 24}=\frac{1}{48}$ $\therefore$ 12 days' work of (16 men + 16 women) $=12(\frac{1}{24}+\frac{1}{48})=12\left(\frac{2+1}{48}\right)=12\times \frac{3}{48}=\frac{3}{4}$
Remaining work = $1-\frac{3}{4}=\frac{1}{4}$ Now (16 men's + 16 women's) 2 days' work = $2(\frac{1}{24}+\frac{1}{48})=2\times \frac{1}{16}=\frac{1}{8}$
$\therefore$ Remaining work =$\frac{1}{4}-\frac{1}{8}=\frac{1}{8}$ $\Rightarrow \frac{1}{384}$ work will be done in 2 days by $(384\times \frac{1}{8}\times \frac{1}{2})=24$ men