There is a crack at the bottom of a tank. Before the crack appeared, Pipe A could fill the tank in 2 hours. Now it takes half an hour longer. How long will the crack take to empty a full tank when Pipe A is kept closed?

A) 10 hours

B) 12 hours

C) 15 hours

D) 9 hours

Correct answer:
A) 10 hours

Description for Correct answer:
Before the crack appeared, Pipe A could fill \( \Large \frac{1}{2} \) the tank in an hour.

Now it takes 2 hours 30 minutes to fill the tank. That is \( \Large \frac{5}{2} \) hours.

Hence, it fills \( \Large \frac{2}{5} \)th of the tank every hour.

The crack at the bottom accounts for this reduction in the amount.

The crack, therefore, drains \( \Large \frac{1}{2}-\frac{2}{5}=\frac{5-4}{10}=\frac{1}{10} \)th of the tank every hour.

As the crack drains a tenth of the tank every hour, it will drain the entire tank in 10 hours if Pipe A is kept closed.


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