An inlet pipe can fill an empty cistern in 8 hours, and an outlet pipe can empty the full cistern in 24 hours. The cistern is empty and both pipes are opened at the same time. In how many hours will the cistern be full?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12 hours
When a filling pipe and an emptying pipe are open together, the cistern gains the difference of their one-hour work. Take the capacity as the LCM of 8 and 24, that is 24 units.
Inlet fills \(\frac{24}{8}=3\) units and outlet empties \(\frac{24}{24}=1\) unit in one hour
Net gain in one hour \(=3-1=2\) units
Time \(\displaystyle =\frac{24}{2}=12\) hours
The cistern is full in 12 hours.