Question : An inlet pipe can fill an empty tank in 51 hours while an outlet pipe drains a filled tank in 76.5 hours. If both the pipes are opened simultaneously when the tank is empty, in how many hours will the tank get filled?
Option 1: 178.5
Option 2: 127.5
Option 3: 102
Option 4: 153
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Correct Answer: 153
Solution :
Given:
An inlet pipe can fill an empty tank in 51 hours while an outlet pipe drains a filled tank in 76.5 hours.
In 1 hour inlet pipe fills = $\frac{1}{51}$ part
In 1 hour outlet pipe empties = $\frac{1}{76.5}$ part
When both open at the same time, in 1 hour the tank fills
$=\frac{1}{51}-\frac{1}{76.5}=\frac{1}{153}$
So, the tank will be filled in 153 hours.
Hence, the correct answer is 153.
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