Discussion
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
Answer: C
Let the capacity be \( C \) litres. The leak alone empties it in 6 hours, so it drains \( \tfrac{C}{6} \) litres an hour.
The inlet adds \( 4 \times 60 = 240 \) litres an hour, and the net effect empties the tank in 8 hours:
\[ \frac{C}{6} - 240 = \frac{C}{8} \]
\[ C\left(\frac{1}{6} - \frac{1}{8}\right) = 240 \quad\Longrightarrow\quad \frac{C}{24} = 240 \]
\[ C = 5760 \text{ litres} \]
The inlet rate must be converted from litres per minute to litres per hour to match the other terms.
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