Pipe A can fill a tank in 14 hours and Pipe B can fill the same tank in 16 hours. Because of a crack at the bottom of the tank, it takes 32 minutes more to fill the empty tank when both the pipes are kept open simultaneously. How long will the crack at the bottom take to drain a full tank if Pipes A and B are kept closed?

A) 108 hours
B) 112 hours

C) 120 hours
D) 130 hours

Correct answer:
B) 112 hours

Description for Correct answer:
Pipe A and Pipe B together can fill \( \Large \frac{1}{14}+\frac{1}{16}=\frac{15}{112} \)th of the tank in an hour. That is they take \( \Large \frac{112}{15} \) hours to fill the tank.

Because of the crack, they will take 32 more minutes or \( \Large \frac{32}{60} \)hours more to fill the tank.

That is \( \Large \frac{112}{15}+\frac{32}{60}= \frac{448 + 32}{60} = \frac{480}{60}= 8 hours \) to fill the tank. Or \( \Large \frac{1}{8} \)th of tank gets filled in an hour.

The crack, therefore, drains \( \Large \frac{15}{112}-\frac{1}{8}=\frac{15-4}{112}=\frac{1}{112} \)th of the tank every hour.

Therefore, the leak alone will take 112 hours to empty the tank.

Please provide the error details in above question

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