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 the cistern get filled?

A) 5 h

B) 7 h

C) 8 h

D) 6 h

Correct answer:
C) 8 h

Description for Correct answer:
Part filled by A in 1 h = \( \Large \frac{1}{4} \)

Part emptied by B in 1 h = \( \Large \frac{1}{8} \)

Part filled by(A + B) in 1 h

= \( \Large \frac{1}{4}+ \left(-\frac{1}{8}\right)=\frac{1}{4}-\frac{1}{8}=\frac{2-1}{8}=\frac{1}{8} \)

Therefore, Required time to fill the cistern = 8 h

Note \( \Large \frac{-1}{8} \) has been taken because it empties the tank.


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