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## Practice Test Discussion

Q)

Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?

• Explanation

Pipe A fills the tank normally in 2 hours
So, Pipe A can fill half of the tank in 1 hour
Let us consider, the leak takes x hours to empty the full tank when pipe A is shut.
So, the leak will empty $\frac{1}{\mathrm{x}}$of the tank in 1 hour.
The net amount of water that gets filled in the tank in 1 hour when pipe A and the leak are open$=\frac{1}{2}-\frac{1}{\mathrm{x}}$ of the tank---Eq 1

As per the question,
when the leak is open, time taken to fill the tank

Therefore, in 1 hour, $\frac{2}{5}$th of the tank gets filled--Eq 2

Equating Eq1 and Eq2, we get

Hence option D is correct.

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