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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?
A) 140Ltrs.
B) 132 Ltrs.
C) 150 Ltrs.
D) 146 Ltrs.
Correct answer:
B) 132 Ltrs.
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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