Haryana Police Constable Model Paper 8

Given:
A swimming pool can be filled by tap P and tap Q together in 36 minutes
P open for 40 minutes and Q open for 30 minutes
Concept:
If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour $=\frac{1}{\mathrm{x}}$ of the total tank.
Calculation:
Let the tap Q fill the tank in ‘a’ minutes.
Part of the swimming pool filled by tap P in 1 minute $=\frac{1}{36}-\frac{1}{\mathrm{a}}$
According to the question,
$\Rightarrow 30\times \frac{1}{\mathrm{a}}+40\left(\frac{1}{36}-\frac{1}{\mathrm{a}}\right)=1$
$\Rightarrow \frac{30}{\mathrm{a}}+\frac{10}{9}-\frac{40}{\mathrm{a}}=1$
$\Rightarrow \frac{40}{\mathrm{a}}-\frac{30}{\mathrm{a}}=\frac{10}{9}-1$
$\Rightarrow \frac{10}{\mathrm{a}}=\frac{1}{9}$
$\Rightarrow \mathrm{a}=90\mathrm{minutes}$
∴ Tap Q can fill the tank in $90$ minutes.