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There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank.
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- 3 h
- 4 h
- 5 h
- 6 h
Correct Option: B
1st pipe takes 1 h to fill 1/2 part of the tank.
So, time taken to fill the whole tank (m) = 2 h
2nd pipe takes 1 h to 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
∴ 1/m + 1/n - 1/x = 7/12 ⇒ 1/2 + 1/3 - 1/x = 7/12
⇒ 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4
∴ x = 4 h
