# CAT Practice : Pipes cisterns, Work time

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Classic Pipes - Cisterns Question!!

## Pipe Leakage

Q.15: ATwo pipes can fill a tank in 12 hrs and 18 hrs respectively. The pipes are opened together but due to a pipe leakage , it takes 48 minutes extra to fill the tank, If the tank is full, what time will it take to completely empty due to the leakage.
1. 72 hrs
2. 84 hrs
3. 96 hrs
4. 112 hrs

Choice A. 72 hrs

## Detailed Solution

Time taken to fill the tank completely without leakage = $\frac{1}{\frac{1}{12} + \frac{1}{18}}$ hrs

= $\frac{1}{\frac{(9 + 6)}{108}} = \frac{108}{15}$ = 7 hours and 12 minutes

Given, it takes 48 minutes extra with the leakage. So, total time taken = 8 hours

= $\frac{1}{\frac{1}{12} + \frac{1}{18} - \frac{1}{x}} = 8$(Where, x is the time taken by the leakage to completely empty the tank)

= ${\frac{1}{12} + \frac{1}{18} - \frac{1}{8}} = \frac{1}{x}$

= $\frac{(9 + 6 - 13.5)}{108} = \frac{1}{x}$

= x = $\frac{108}{1.5}$ = 72 hours

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## More questions from Pipes Cisterns, Work Time

Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.