Two pipes A and B can fill a tank in 10 minutes & 16 minutes respectively whereas a waste pipe can empty 3 litres per minute. All the three pipes working together can fill the tank in 8 minutes, then the capacity of the tank is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 80 litres
Let the waste pipe empty a fraction w of the tank per minute. In terms of the fraction of the tank filled per minute:
\( \displaystyle \frac{1}{10}+\frac{1}{16}-w=\frac{1}{8} \)
\( \displaystyle w=\frac{8}{80}+\frac{5}{80}-\frac{10}{80}=\frac{3}{80} \)
So the waste pipe empties \( \frac{3}{80} \) of the tank per minute, which is 3 litres. Hence the whole tank holds
\( \displaystyle 3\times\frac{80}{3}=80\ \text{litres} \)
Shortcut: Check Option (2) with a capacity of 80 litres: A fills 8 L/min, B fills 5 L/min and the waste pipe empties 3 L/min, so the net rate is 10 L/min and 80 L fill in 8 minutes.