A cistern can be filled up in 4 h by an inlet A. An outlet

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A cistern can be filled up in 4 h by an inlet A. An outlet B can empty the cistern in 8 h. If both A and B are opened simultaneously, then after how much time will the cistern get filled?

1. 5 h
2. 7 h
3. 8 h
4. 6 h

Correct Option: C

Part filled by A in 1 h = 1/4
Part emptied by B in 1 h = 1/8
Part filled by (A + B) In 1 h = 1/4+ ( -1/8 ) = 1/4 - 1/8 = (2 - 1)/8 = 1/8
∴ Required time to fill the cistern = 8