Pipes A and B are filling pipes while pipe C is an emptying pipe. A and B can fill a tank in 72 and 90 minutes respectively. When all the three pipes are opened together, the tank gets filled in 2 hours. A and B are opened together for 12 minutes, then closed and C is opened. The tank will be empty after:
18 minutes
Step 1 — Rates: A fills at \(\tfrac{1}{72}\)/min, B at \(\tfrac{1}{90}\)/min, so
\[A+B=\tfrac{1}{72}+\tfrac{1}{90}=\tfrac{5+4}{360}=\tfrac{1}{40}\text{ /min}\]
All three together fill in 120 min, giving \(A+B+C=\tfrac{1}{120}\). Hence C's rate \(=\tfrac{1}{120}-\tfrac{1}{40}=-\tfrac{1}{60}\)/min (empties \(\tfrac{1}{60}\) per minute).
Step 2 — Tank filled in 12 min by A+B: \(\tfrac{1}{40}\times 12=\tfrac{3}{10}\).
Step 3 — Time for C to empty: \(\dfrac{3/10}{1/60}=\dfrac{3}{10}\times 60=18\) min.
Therefore the tank is empty after 18 minutes.
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