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A pipe can fill a cistern in 6 hours. Due to leakage in the cistern, it takes 3 hours more to fill the tank. If the cistern is full, then time taken by the leakage to empty the cistern is

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2 hours

15 hours

18 hours

20 hours

answer is C.

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Detailed Solution

Let the time taken by the leakage to empty the cistern be t hours, then

$\begin{array}{l} \frac{1}{6} - \frac{1}{t} = \frac{1}{9} \Rightarrow \frac{1}{t} = \frac{1}{6} - \frac{1}{9} \\ \Rightarrow \frac{1}{t} = \frac{1}{18} \Rightarrow t = 18 \end{array}$

$∴$ Option (c) is the correct answer.

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