Question

A swimming pool can be filled in $4$ hours by $8$ pumps of the same type. How many such pumps are required, if the pool is to be filled in $2\frac{2}{3}$ hours?
[3 marks]

Answer 1

Let the number of pump which can fill the pool in $2\frac{2}{3}$ hours be $x$.

Number of Pumps	$8$	$x$
Time required to fill the swimming pool (in hours)	$4$	$2\frac{2}{3}$

Since the time required to fill the swimming pool is reduced to $2\frac{2}{3}$ hours, the number of pumps required will be more.

Hence, the number of pumps ($P$) and time required to fill them ($T$) are in inverse proportion.
$\Rightarrow PT=constant$
$\Rightarrow P_1{T}_1=P_2{T}_2$

[1.5 marks]

$\Rightarrow 8\times 4=x\times \frac{8}{3}$
$\Rightarrow x=\frac{8\times 4\times 3}{8}=12$ pumps

Therefore, $12$ pumps will be required to fill the swimming pool in $2\frac{2}{3}$ hours.

[1.5 marks]