A tap can fill a tank in 8 minutes and another tap can empty the same tank in…
2022
A tap can fill a tank in 8 minutes and another tap can empty the same tank in 16 minutes. If both taps are opened simultaneously when the tank is empty, in how much time will the tank be full?
- A.
After 32 minutes
- B.
After 24 minutes
- C.
After 16 minutes
- D.
None of these
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept
In pipe-and-cistern problems, model each pipe by its per-minute rate, where the whole tank counts as 1 unit of work. A pipe that fills the tank alone in T minutes works at +1/T per minute; an emptying pipe works at -1/T per minute. With several pipes open together, add the signed rates to get the net rate, and the time to fill the tank is 1 divided by that net rate.
Application
Filling pipe rate: it fills the whole tank in 8 minutes, so its rate is +1/8 of the tank per minute.
Emptying pipe rate: it empties the whole tank in 16 minutes, so its rate is -1/16 of the tank per minute.
Net rate with both open: 1/8 - 1/16 = 2/16 - 1/16 = 1/16 of the tank per minute (positive, so the tank does fill).
Time to fill = 1 / (1/16) = 16 minutes.
Cross-check
In 16 minutes the filling pipe pours in 16 / 8 = 2 tank-volumes while the emptying pipe drains 16 / 16 = 1 tank-volume. The leftover is 2 - 1 = 1 full tank, which confirms the tank is exactly full at 16 minutes.