Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, then how much time will be needed to make the tank full?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(15\displaystyle\frac{5}{13}\) hours
In one hour A fills \(\frac{1}{20}\) of the tank, B fills \(\frac{1}{25}\) and C empties \(\frac{1}{40}\). The net filling rate is
\( \displaystyle \frac{1}{20} + \frac{1}{25} - \frac{1}{40} = \frac{10 + 8 - 5}{200} = \frac{13}{200} \)
So the time to fill the tank is
\( \displaystyle \frac{200}{13} = 15\frac{5}{13} \text{ hours} \)
(since \(13 \times 15 = 195\), the remainder is 5).