A filling pipe can fill an empty tank in 24 minutes, and an emptying pipe can empty the full tank in 36 minutes. The tank is one-fourth full when both pipes are opened at the same time. In how many minutes will the tank be full?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 54 minutes
The tank already holds one-fourth, so the pipes only have to fill the remaining three-fourths at their net rate.
Net part filled in one minute \(\displaystyle =\frac{1}{24}-\frac{1}{36}=\frac{3-2}{72}=\frac{1}{72}\)
Part to be filled \(\displaystyle =1-\frac{1}{4}=\frac{3}{4}\)
Time \(\displaystyle =\frac{3}{4}\times72=54\) minutes