Pipes A and B can fill an empty tank in 20 minutes and 30 minutes respectively. When an outlet pipe C is opened along with A and B, the water level in the tank does not change. In how many minutes can pipe C alone empty the full tank?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12 minutes
The level does not change, so pipe C takes out water exactly as fast as A and B together put it in.
\(\displaystyle \text{Part filled by A and B in 1 minute} = \frac{1}{20} + \frac{1}{30}\)
\(\displaystyle \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{1}{12}\)
So pipe C empties \(\frac{1}{12}\) of the tank in 1 minute and would empty the full tank in 12 minutes.
Why the other options are incorrect
Option (1) 50 minutes — Incorrect. This adds the two times; the parts filled per minute must be added, not the times.
Option (2) 25 minutes — Incorrect. This is the average of the two times; C must match the combined rate of A and B, which is faster than either pipe.
Option (4) 10 minutes — Incorrect. C would then take out \(\frac{1}{10}\) of the tank per minute, more than the \(\frac{1}{12}\) that A and B put in, so the level would fall.