Discussion
A cistern is normally filled in 8 hours but takes another 2 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in
Answer: D
The leak would empty the full cistern in 40 hours.
Without the leak the cistern fills in 8 hours; with it, in 10. The leak's rate is the difference between the two filling rates:
\[ \frac{1}{8} - \frac{1}{10} = \frac{5 - 4}{40} = \frac{1}{40} \]
The leak empties 1/40 of the cistern per hour, so 40 hours to empty it. 16, 20 and 25 hours do not satisfy this; for example, a 20-hour leak would give a net rate of 1/8 - 1/20 = 3/40 and a filling time of 13.3 hours.
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