A tank is full of water. An outlet pipe can empty the full tank in 8 hours, and an inlet pipe can fill the empty tank in 12 hours. Both pipes are opened at the same time on the full tank. In how many hours will the tank be empty?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24 hours
The outlet is faster, so the tank loses the outlet's one-hour work minus the inlet's one-hour work. Take the capacity as the LCM of 8 and 12, that is 24 units.
Outlet empties \(\frac{24}{8}=3\) units and inlet fills \(\frac{24}{12}=2\) units in one hour
Net loss in one hour \(=3-2=1\) unit
Time to empty \(\displaystyle =\frac{24}{1}=24\) hours
The tank is empty in 24 hours.