**Question:**

*Mark (✓) against the correct answer:*

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

(a) 7 hours

(b) 14 hours

(c) 8 hours

(d) 3 hours

**Solution:**

(b) 14 hours

A pump fills a tank in 2 hours.

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

Let $\mathrm{x}$ hours be the time required for water to leak from the cistern.

Part of tank drained by the leak in one hour $=-\frac{1}{x}$

Time required to fill the leaking cistern $=2 \frac{1}{3}=\frac{7}{3}$ hours

Part of tank stored with water in one hour $=\frac{3}{7}$

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

$\frac{1}{\mathrm{x}}=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14}$

$\mathrm{x}=14$ hours