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 of the tank be $C$ liters.
Rate of first pipe = $\frac{C}{6}$ liters/min
Rate of second pipe = $\frac{C}{12}$ liters/min
Rate of third pipe (emptying) = 18 liters/min
All working together fill the tank in 5 minutes:
Net rate × time = capacity
$(\frac{C}{6} + \frac{C}{12} - 18) \cdot 5 = C$
$\frac{2C}{12} + \frac{C}{12} - 18 = \frac{3C}{12} - 18 = \frac{C}{4} - 18$
$5(\frac{C}{4} - 18) = C$
$\frac{5C}{4} - 90 = C \Rightarrow \frac{5C}{4} - C = 90 \Rightarrow \frac{C}{4} = 90$
$C = 360$ liters
Capacity of the tank = 360 liters