An electric pump can fill a tank in $3$ hours. Because of a leak in the tank, it took $3\frac{1}{2}$ hours to fill the tank. If the tank is full, how much time will the leak take to empty it ?

A) 21 hours

B) 20 hours

C) 30 hours

D) 40 hours

E) 50 hours


Option A


Work done by the leak in 1 hour $=\left[\frac{1}{3}-\frac{1}{\left(\frac{7}{2}\right)}\right]$

$=\frac{1}{3}-\frac{2}{7}$ $=\frac{1}{21}$

The leak will empty the tank in 21 hours.