Two pipes can fill a tank in 12 hours and 4 hours respectively. A third pipe alone can empty the completely filled tank in 5 hours. If all the three pipes are opened simultaneously, then how much time (in hours) will it take for the empty tank to get filled?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(7\frac{1}{2}\)
Work is counted as the part of the tank done in one hour. The two filling pipes add their parts, and the emptying pipe takes its part away.
In 1 hour the pipes fill \(\frac{1}{12}\) and \(\frac{1}{4}\) of the tank, and the third pipe empties \(\frac{1}{5}\)
Part filled in 1 hour with all three open: \(\displaystyle \frac{1}{12}+\frac{1}{4}-\frac{1}{5}=\frac{5+15-12}{60}=\frac{8}{60}=\frac{2}{15}\)
Time to fill the whole tank: \(\displaystyle \frac{15}{2}=7\frac{1}{2}\) hours