Question

A pond is dug in 4 days and requires 12 men. If there is an inverse relationship between the number of men required to dig a well and the number of days, calculate the number of men required to dig the well in 1 day.

• A. 12
• B. 48
• C. 36
• D. 49

Answer 1

The correct option is B 48

Let the number of days requires to dig a pond be $D$ and the number of men required to dig the pond be $M$.

$\text{Given that}D\propto \frac{1}{M}$
$\Rightarrow D=\frac{k}{M}$ ; where $k$ is a constant

According to the question,
A pond is dug in 4 days which requires 12 men
i.e. $D=4,M=12$
We know,
$D=\frac{k}{M}\Rightarrow 4=\frac{k}{12}\Rightarrow k=48$

Now, if the pond has to be dug in 1 day,
i.e. $D=1,M=?$
We know,
$D=\frac{k}{M}$
$\Rightarrow 1=\frac{48}{M}$ $(\because k=48)$
$\Rightarrow M=48$

Hence, 48 men are required to dig the pond in 1 day.