Pipe A alone can fill a tank in 12 minutes and Pipe B can fill the same tank in 15 minutes. Pipe C which is at the bottom of the tank can drain the tank at the rate of 22 litres/minute. If all three pipes are kept open together when the tank is full, the tank gets emptied in one hour. What is the capacity of the tank?
Correct Answer: Description for Correct answer:
Let C be the lime that Pipe C takes to empty the tank when Pipe A and Pipe B are closed.
Pipe A + Pipe B - Pipe C kept Open together results in a full tank getting emptied in 1 hour (60 min.)
\( \Large \frac{1}{12}+\frac{1}{15}-\frac{1}{C} = -\frac{1}{60} \) (negative sign indicates that the tank is getting emptied) or \( \Large \frac{1}{12}+\frac{1}{15}-\frac{1}{C}=\frac{1}{C}\ or\ C = 6\ minutes \)
If Pipe C can empty the tank in 6 minutes and it drains water at the rate of 22 liters/minute, then the capacity of the tank = \( \Large 6 \times 22 \) = 132 liters.
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