Two pipes can fill a tank in 12 and 15 minutes respectively and a waste pipe can empty 3.4 litres per minute. All the three pipes working together can fill the tank in 18 minutes. The capacity of the tank is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36 litres
Let the capacity be C litres. In one minute the two filling pipes add \( \frac{C}{12} \) and \( \frac{C}{15} \), the waste pipe removes 3.4 litres, and all three together fill \( \frac{C}{18} \).
\( \displaystyle \frac{C}{12}+\frac{C}{15}-3.4=\frac{C}{18} \)
Collecting the terms in C,
\( \displaystyle C\left(\frac{1}{12}+\frac{1}{15}-\frac{1}{18}\right)=3.4 \)
\( \displaystyle C\cdot\frac{15+12-10}{180}=3.4 \)
\( \displaystyle C\cdot\frac{17}{180}=3.4 \)
\( \displaystyle C=\frac{3.4\times180}{17} \)
\( \displaystyle =36 \)