Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 litres per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 120 litres
Let the capacity of the tank be C litres. The work done in one minute by the three pipes together is \( \frac{C}{15} \):
\( \displaystyle \frac{C}{20}+\frac{C}{24}-3=\frac{C}{15} \)
\( \displaystyle C\left(\frac{1}{20}+\frac{1}{24}-\frac{1}{15}\right)=3 \)
\( \displaystyle C\cdot\frac{6+5-8}{120}=3 \)
\( \displaystyle \frac{C}{40}=3 \)
\( \displaystyle C=120\text{ litres} \)