Two pipes can fill a tank in 20 minutes and 24 minutes respectively, and a waste pipe can empty 3 gallons of water per minute. If all the three pipes working together can fill the tank in 15 minutes, then the capacity of the tank is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 120 gallons
Let the work of each pipe be measured in fractions of the tank per minute.
\( \displaystyle \text{Two filling pipes}:\ \frac{1}{20}+\frac{1}{24}=\frac{6+5}{120} \)
\( \displaystyle =\frac{11}{120} \)
\( \displaystyle \text{All three pipes}:\ \frac{1}{15}=\frac{8}{120} \)
The waste pipe therefore empties
\( \displaystyle \frac{11}{120}-\frac{8}{120}=\frac{3}{120} \text{ of the tank per minute} \)
This part equals 3 gallons, so \( \frac{1}{120} \) of the tank is 1 gallon, and the capacity is 120 gallons.
Shortcut: Check Option (4) with a 120-gallon tank: the pipes fill 6 and 5 gallons per minute, the waste pipe removes 3, net 8 gallons per minute, so the tank fills in \( \frac{120}{8}=15 \) minutes.