The overhead tank of a building is filled by two supply pipes, X and Y, which can fill the empty tank in 3 hours and 4 hours respectively. A third pipe, Z, which carries water to the flats, can empty the full tank in 6 hours. The tank is empty when all three pipes are opened at the same time. How long will it take for the tank to be full?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 hours 24 minutes
Take the capacity as the LCM of 3, 4 and 6, that is 12 units. The supply pipes add units each hour and pipe Z takes units away.
X fills \(12\div3=4\) units and Y fills \(12\div4=3\) units per hour
Z empties \(12\div6=2\) units per hour
Net gain with all three open \(=4+3-2=5\) units per hour
Time to fill \(\displaystyle=\frac{12}{5}=2\frac{2}{5}\) hours
\(\frac{2}{5}\) hour \(=\frac{2}{5}\times60=24\) minutes
The tank is full in 2 hours 24 minutes.