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An empty tank can be filled by two pipes individually in 30 min and 60 min respectively. There is a leak pipe which can be empty a full tank in 45 min. If all the three pipes are open, how much time does it take fill an empty tank? (in minutes)

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Detailed Solution

Two pipes can be filled $= \frac{1}{30} + \frac{1}{60}$

a leak pipe = $\frac{1}{45}$

Time taken to fill $= \frac{1}{30} + \frac{1}{60} - \frac{1}{45}$

$\Rightarrow \frac{6 + 3 - 4}{180} \Rightarrow \frac{5}{180} = \frac{1}{36} \min$

Time taken to fill an empty tank in 36 min

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