Numerical answer
Pipe A can fill an empty tank in 10 hours and pipe B can fill it in 15 hours, while pipe C can empty the full tank in 12 hours. All three pipes are opened together on the empty tank. After 2 hours, pipe C is closed. In how many hours from the start will the tank be full?
Show answer and solution
Answer: 7
Take the tank capacity as LCM(10, 15, 12) = 60 units. Rates: A = 6, B = 4, C = −5 units/hour.
First 2 hours (all open): (6 + 4 − 5) × 2 = 10 units filled.
Remaining 50 units are filled by A and B at 10 units/hour → 5 hours.
Total time = 2 + 5 = 7 hours.
Tip: Using an LCM capacity turns fraction arithmetic into integer arithmetic and is much faster under exam pressure.
First 2 hours (all open): (6 + 4 − 5) × 2 = 10 units filled.
Remaining 50 units are filled by A and B at 10 units/hour → 5 hours.
Total time = 2 + 5 = 7 hours.
Tip: Using an LCM capacity turns fraction arithmetic into integer arithmetic and is much faster under exam pressure.
Saved on this device. Sign in or create a free account to keep it on every device.