Question

If 200 men can complete a piece of work in 4 days, then find the time required to complete the same work by 50 men.

• A. 12 days
• B. 14 days
• C. 16 days
• D. 18 days

Answer 1

The correct option is C 16 days

The number of men (N) employed to complete a piece of work is inversely proportional to the number of days (D).

$\Rightarrow N\propto \frac{1}{D}$

Let the constant of variation be k.
$\Rightarrow N=\frac{k}{D}$
$\Rightarrow ND=k$
Given, when N = 200 men , D = 4 days.
So, $k=ND=\left(200\right)\left(4\right)=800$
$\Rightarrow N=\frac{800}{D}$
Hence, the time required (D) to complete the same work by 50 men $=\frac{800}{50}=16\text{days}.$