Question

A workforce of 210 men with a supervisor can finish a certain piece of work in 5 months. How many extra men must he employ if he want to complete job in just 2 months?
[2 marks]

Answer 1

Let the extra men employed be $x$.

Number of men	$210$	$x$
Time (in months)	$5$	$2$

As number of men [M] will increase, the time duration [D] to finish a work will be less.
Hence, it is a case of inverse proportion.
$\Rightarrow MD=constant$
$\Rightarrow M_1{D}_1=M_2{D}_2$

[0.5 mark]

$\Rightarrow 210\times 5=x\times 2$
$\Rightarrow x=\frac{210\times 5}{2}=525$

Therefore, the required number of men to finish the work in $2$ months is $525$ men, i.e. $315$ extra men needed.

[1.5 marks]