A contractor undertook to build a road in $200$ days. He employed $140$ men. After $60$ days, he found that only one-fourth of the road could be built. How many additional men should he employ to complete the work in time?

The correct option is A. $40$

Amount of work remaining $=1-\frac{1}{4}=\frac{3}{4}$ units of work

Now, no. of days in which the remaining work needs to be completed $=200-140=60$ days

Let there be extra $x$ men required to finish the work on time.

Now, efficiency of each of men

Since, efficiency of each men will remain same, therefore,

$\frac{\text{No. of men initially hired}\times \text{No. of days they worked}}{\text{Amount of work completed}}=\frac{\text{No. of men now required}\times \text{No of days}}{\text{Work that is pending}}$

$\Rightarrow \frac{140\times 60}{\frac{1}{4}}=\frac{(140+x)\times 140}{\frac{3}{4}}$

$\Rightarrow 3\times 60=140+x$

$\Rightarrow x=40$