Sixteen men can complete a work in 24 days. Twenty four women can complete the same work in 32 days. Sixteen men and sixteen women together worked for twelve days, after which women dropped. How many more men are to be taken to complete the remaining work in 2 days?

Correct option is A

Given:

16 men can complete a work in 24 days

24 women can complete the same work in 32 days.

Formula Used:

Total work = number of days $$\times$$ efficiency

Solution:

Let efficiency of men = m

Let efficiency of woman = w

According to question

​$$16\times24\times m=24\times32\times w$$

​$$\frac{m}{w}= \frac{2}{1}$$ 

So efficiency of men = 2t

efficiency of woman = t

Total work = $$16\times24\times 2t =768t$$ 

Work done by Sixteen men and sixteen women together worked for twelve days= $$(16\times 2t +16\times t)\times 12 days =576t$$ 

Remaining work = 768t - 576t = 192t

Total men required to complete 192t work in 2 days = $$\frac{192t}{2\times 2t}=48$$​ men

More men required = 48 -16 =32 men

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