Question

A swimming pool can be filled in $3$ hours by $10$ pumps of the same type. How many such pumps are required, if the pool is to be filled in $1\frac{1}{2}$ hours?
[2 marks]

Answer 1

Let the number of pump which can fill the pool in $1\frac{1}{2}$ hours be $x$.

Number of Pumps	$10$	$x$
Time required to fill the swimming pool (in hours)	$3$	$1\frac{1}{2}$

[0.5 mark]

Since the time required to fill the swimming pool is reduced to $1\frac{1}{2}$ hours, the number of pumps required will be more.

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

[0.5 mark]

$\Rightarrow 10\times 3=x\times \frac{3}{2}$
$\Rightarrow x=\frac{10\times 3\times 2}{3}=20$ pumps

Therefore, $20$ pumps will be required to fill the swimming pool in $1\frac{1}{2}$ hours.

[1 mark]