A pump can fill a tank with water in 2 hours. Because of a leakage it took $21/3$ hours to fill the tank. How much time will it take for the leakage to drain all the water of the full tank ?

14 hours

The correct answer is option (3) : 14 hours

Let the leakage take x hrs to drain all the water of full tank.

So, part of the tank drained by leakage in 1 hr $=\frac{1}{x}$

Part of the tank filled by the pump in 1 hr $=\frac{1}{2}$

Given, when both pump and leakage working together, it took $2\frac{1}{3}$ hrs. i.e $\frac{7}{3}hrs$ to fill the tank.

So, part of the tank filled by both in 1 hr $=\frac{3}{7}$

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

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

$\frac{1}{x}=\frac{1}{14}⇒x=14$

Hence the leakage will take 14 hrs to drain the water of the full tank.