Two inlet pipes can fill an empty tank in 10 minutes and 15 minutes respectively. A waste pipe at the bottom lets out 7 litres of water per minute. When the tank is empty and all three pipes are opened together, the tank is full in 9 minutes. What is the capacity of the tank?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 126 litres
The waste pipe takes away the difference between the two inlets' joint rate and the net rate, and this difference is given as 7 litres per minute.
Both inlets fill \(\displaystyle \frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{1}{6}\) of the tank per minute
All three pipes fill \(\frac{1}{9}\) of the tank per minute
Waste pipe lets out \(\displaystyle \frac{1}{6}-\frac{1}{9}=\frac{3-2}{18}=\frac{1}{18}\) of the tank per minute
\(\frac{1}{18}\) of the tank \(=7\) litres, so the capacity \(=7\times18=126\) litres
The tank holds 126 litres.