Question

A work-force of $420$ men with a contractor can finish a certain piece of work in $9$ months. How many extra men must he employ to complete the job in $7$ months $?$

Answer 1

Step: Calculate the extra men required

Given: $420$ men can finish the work in $9$ months

Let the number of men required to complete the work in $7$ months be $‘x^{\prime }$

Number of men	$420$	$x$
Number of months	$9$	$7$

Clearly, more is the number of men, less will be the number of months to finish the same work. It is, therefore, the case of inverse variation.
$\Rightarrow$ Ratio of number of men $=$ Inverse ratio of number of months

$\Rightarrow \frac{420}{x}=\frac{7}{9}$
$\Rightarrow x=9\times 60$
$\Rightarrow x=540$
$\Rightarrow \text{Extra men}=540–420=120$

Hence, $120$ extra men are required to finish the work in $7$ months.