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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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