Question

If 10 boys can complete a piece of work in 5 days, then find the time required to complete the same work by 2 boys.

• A. 25 days
• B. 5 days
• C. 10 days
• D. 50 days

Answer 1

The correct option is A 25 days

The number of boys (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 = 10 boys , D = 5 days.
So, $k=ND=\left(10\right)\left(5\right)=50$
$\Rightarrow N=\frac{50}{D}$
Hence, the time required (D) to complete the same work by 2 boys $=\frac{50}{N}=\frac{50}{2}=25days.$