Tick (✓) the correct answer:

Question:

Tick (✓) the correct answer:

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) $2 \frac{1}{3}$ hours

(b) 7 hours

(c) 8 hours

(d) 14 hours

Solution:

(d) 14 hours

A pump can fill a tank in 2 hours.

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

Suppose the leak empties a full tank in x hours.

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

Part of tank filled in one hour $=\frac{1}{2}-\frac{1}{x}=\frac{3}{7}$ (given)

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

$\mathrm{x}=14$ hours

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