Question

10 men can complete a piece of work in 10 days. In how many days will 5 men complete the same work.

• A. 20 days
• B. 10 days
• C. 5 days
• D. 15 days

Answer 1

The correct option is A 20 days

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

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

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

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

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

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

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

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

Let the number of days required to complete the same work by 5 men be x days.

$Hence,\frac{\left(10\right)\left(10\right)}{W}=\frac{\left(5\right)\left(x\right)}{W}$

So, x = 20 days.