There are three pipes connected with a tank. The first pipe can fill \( \Large \frac{1}{2} \) part of the tank in 1 h, second pipe can fill \( \Large \frac{1}{3} \) part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, \( \Large \frac{7}{12} \) part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank?

A) 3 h

B) 4 h

C) 5 h

D) 6 h

Correct answer:
B) 4 h

Description for Correct answer:
1st pipe takes 1 h to fill \( \Large \frac{1}{2} \) part of the tank.

So, time taken to fill the whole tank (m) = 2 h

2nd pipe takes 1 h to \( \Large \frac{1}{3} \) part of the tank

So. time taken to fill the whole tank (n) = 3 h

Let 3rd pipe takes P h to empty the tank = x

Therefore, \( \Large \frac{1}{m} \)+ \( \Large \frac{1}{n} \)- \( \Large \frac{1}{x} \)= \( \Large \frac{7}{12} \)

= \( \Large \frac{1}{2} \)+ \( \Large \frac{1}{3} \)- \( \Large \frac{1}{x} \) = \( \Large \frac{7}{12} \)

= \( \Large \frac{1}{x}=\frac{6+4-7}{12}=\frac{3}{12}=\frac{1}{4} \)

Therefore, x = 4 h


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