Question

$24$ men can complete a work in $16$ days. $32$ women can complete the same work in $24$ days. $16$ men and $16$ women worked for $12$ days. How many more men are required to complete the remaining work in $2$ days ?

• A. $24$
• B. $36$
• C. $32$
• D. None of these

Answer 1

The correct option is A $24$

24 men can complete in 16 days $=100\%$ work.
So, one man can complete in 16 days $=\frac{100}{24}\%$ of work
One man can complete in 1 day $=\frac{100}{16\times 24}=0.26\%$ work
One women can complete in 1 day $=\frac{100}{24\times 32}=0.13\%$ work
One women and one men can complete in 1 day $=0.26+0.13=0.39\%$ work
So, 16 man and 16 women can complete in 12 days $=0.39\times 12\times 16=75\%$ work
Rest Work $=25\%$
To complete $25\%$ work in 2 days, no. of men required $=\frac{24}{2\times 0.26}=48$ men
So, extra men $=48-24=24.$