Numerical answer
Pipes A and B can fill an empty tank in 15 minutes and 20 minutes respectively, while pipe C can empty the full tank in 10 minutes. All three pipes are opened together on the empty tank, and after 4 minutes pipe C is closed. In how many minutes, from the start, will the tank be full?
Show answer and solution
Answer: 12
Take tank capacity = 60 units (LCM of 15, 20, 10). A fills 4 units/min, B fills 3 units/min, C empties 6 units/min.
With all three open, net rate = 4 + 3 − 6 = 1 unit/min. In 4 minutes, 4 units are filled.
Remaining 56 units are filled by A and B together at 7 units/min, taking 8 minutes.
Total time = 4 + 8 = 12 minutes.
Tip: Use a capacity equal to the LCM of the individual times so every pipe's rate is an integer.
With all three open, net rate = 4 + 3 − 6 = 1 unit/min. In 4 minutes, 4 units are filled.
Remaining 56 units are filled by A and B together at 7 units/min, taking 8 minutes.
Total time = 4 + 8 = 12 minutes.
Tip: Use a capacity equal to the LCM of the individual times so every pipe's rate is an integer.
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