Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 360 litres
Let the capacity be C litres. The filling pipes add \(\frac{C}{6}\) and \(\frac{C}{12}\) litres per minute, and the third pipe removes 18 litres per minute. The net rate is
\( \displaystyle \frac{C}{6} + \frac{C}{12} - 18 = \frac{3C}{12} - 18 = \frac{C}{4} - 18 \)
Together they fill the tank in 5 minutes, so net rate × time = capacity:
\( \displaystyle 5\left(\frac{C}{4} - 18\right) = C \)
\( \displaystyle \frac{5C}{4} - 90 = C \)
\( \displaystyle \frac{C}{4} = 90 \)
\(C = 360\)
So the tank holds 360 litres.