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

Answer 1

(b) 14 hours

​$$\begin{gathered} \mathrm{A}\mathrm{pump}\mathrm{fills}\mathrm{a}\mathrm{tank}\mathrm{in}2\mathrm{hours}. \\ \text{Part of tank filled by the pump in one}\mathrm{hour}=\frac{1}{2} \\ \mathrm{Let}\mathrm{x}\mathrm{hours}\mathrm{be}\mathrm{the}\mathrm{time}\mathrm{required}\mathrm{for}\mathrm{water}\mathrm{to}\mathrm{leak}\mathrm{from}\mathrm{the}\mathrm{cistern}. \\ \text{Part of tank drained by the leak in one hour}=-\frac{1}{\mathrm{x}} \\ \mathrm{Time}\mathrm{required}\mathrm{to}\mathrm{fill}\mathrm{the}\mathrm{leaking}\mathrm{cistern}=2\frac{1}{3}=\frac{7}{3}\mathrm{hours} \\ \text{Part of tank stored with water in one hour}=\frac{3}{7} \\ \Rightarrow \frac{3}{7}=\frac{1}{2}-\frac{1}{\mathrm{x}} \\ \frac{1}{\mathrm{x}}=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14} \\ \mathrm{x}=14\mathrm{hours} \end{gathered}$$