Question

A contractor undertook a contract to complete a part of a stadium in $9$ months with a team of $560$ persons. Later on, it was required to complete the job in $5$ months. How many extra persons should he employ to complete the work?
[4 marks]

Answer 1

Let the number of workers who can complete the work in $5$ months be $x$.

Number of workers	$560$	$x$
Time (in months)	$9$	$5$

To complete the job in less time implies that more persons have to be employed.

[0.5 mark]

Hence, the number of workers ($W$) and number of months ($M$) are in inverse proportion.
$\Rightarrow WM=constant$
$\Rightarrow W_1{M}_1=W_2{M}_2$

[1.5 marks]

$\Rightarrow 560\times 9=x\times 5$
$\Rightarrow x=\frac{560\times 9}{5}=1008$ workers

[1 mark]

Thus, $1008$ workers are required to complete the work in $5$ months.
$\Rightarrow 1008-560=488$ workers
Therefore, $448$ more workers are required.

[1 mark]