Question

If 100 men can complete a piece of work in 2 days, then find the time required to complete the same work by 25 men.

• A. 8 days
• B. 12 days
• C. 16 days
• D. 4 days

Answer 1

The correct option is A 8 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 = 100 men , D = 2 days.
So, $k=ND=\left(100\right)\left(2\right)=200$
$\Rightarrow N=\frac{200}{D}$
Hence, the time required (D) to complete the same work by 25 men $=\frac{200}{25}=8days.$