A pump can fill a tank with water in 2 hours, because of leakage it took $2 \frac{1}{3}$ hours to fill the tank. In how many hours the leak can drain all the water of tank?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 14
$\text{Pump rate} = \frac{1}{2} \text{ tank/hour}$
$\text{Time with leak} = 2\frac{1}{3} = \frac{7}{3} \text{ hours}$
$\text{Net rate} = \frac{1}{\frac{7}{3}} = \frac{3}{7}$
$\text{Leak rate} = \frac{1}{2} - \frac{3}{7}$
$= \frac{7 - 6}{14} = \frac{1}{14}$
$\text{Time taken by leak alone} = 14 \text{ hours}$
The leak can drain the tank in $14$ hours.