Discussion
A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty the cistern in
Answer: D
Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).
With the leak the cistern takes \( 10 + 5 = 15 \) hours.
\[ \frac{1}{10} - \frac{1}{L} = \frac{1}{15} \]
\[ \frac{1}{L} = \frac{3 - 2}{30} = \frac{1}{30} \quad\Longrightarrow\quad L = 30 \text{ hours} \]
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