An inlet pipe can fill an empty tank in 30 minutes. An outlet pipe at the bottom drains water at 5 litres per minute. When the tank is empty and both pipes are opened together, the tank is full in 45 minutes. What is the capacity of the tank?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 450 litres
Let the capacity be \(C\) litres. The outlet takes away the difference between the inlet's rate and the net rate, and this difference is given as 5 litres per minute.
Inlet alone: \(\frac{C}{30}\) litres per minute
Both open: \(\frac{C}{45}\) litres per minute
Outlet rate \(\displaystyle =\frac{C}{30}-\frac{C}{45}=\frac{3C-2C}{90}=\frac{C}{90}\) litres per minute
\(\displaystyle \frac{C}{90}=5\), so \(C=450\)
The tank holds 450 litres.