Question

A pump can fill a tank in 2 hours. Due to a leak in the tank It takes $2\frac{1}{3}$ hours to fill the tank. The leak can empty the full tank in

(a) 21 hours

(b) 7 hours

(c) 8 hours

(d) 14 hours

Answer 1

First pump's 1 hour work to fill $=\frac{1}{2}$

Due to leakage, tank is filled in $2\frac{1}{3}$ hour

$=\frac{7}{3}hrs.$

or both its one hour work $=\frac{3}{7}$

$\therefore$ Leakage's 1 hour work to empty the tank

$=\frac{1}{2}-\frac{3}{7}$

$=\frac{7-6}{14}=\frac{1}{14}$

$\therefore$ Leak will empty the tank in 14 hours