Question

25 boys can complete a piece of work in 6 days. In how many days will 75 men complete the same work?

• A. 2 days
• B. 4 days
• C. 8 days
• D. 16 days

Answer 1

The correct option is A 2 days

The number of boys (B) required to complete a work is directly proportional to the amount of work (W).

$B\propto W$...(1)

The number of boys (B) required to complete a work is inversely proportional to the number of days required to do the work (D).

$B\propto \frac{1}{D}$...(2)

Combining (1) and (2), we get,

$B\propto \frac{W}{D}$

Let k be the constant of variation.
$So,B=k\frac{W}{D}$

$\Rightarrow \frac{BD}{W}=K\left(constant\right)$

Let the number of days required to complete the same work by 75 boys be x days.

$Hence,\frac{\left(25\right)\left(6\right)}{W}=\frac{\left(75\right)\left(x\right)}{W}$

$\Rightarrow 150=75x$
$So,x=2days$