A tank is three-fourths full of water. An inlet pipe can fill the empty tank in 16 minutes, and an outlet pipe can empty the full tank in 8 minutes. Both pipes are opened at the same time. In how many minutes will the tank be empty?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12 minutes
The outlet is faster, so the tank loses the outlet's one-minute work minus the inlet's one-minute work, and only the three-fourths already in it has to be let out.
Net part emptied in one minute \(\displaystyle =\frac{1}{8}-\frac{1}{16}=\frac{2-1}{16}=\frac{1}{16}\)
Part to be emptied \(=\frac{3}{4}\)
Time \(\displaystyle =\frac{3}{4}\times16=12\) minutes
The tank is empty in 12 minutes.