Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third…
2025
Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe can empty the full tank in 20 hours. If all three pipes are opened together, in how many hours will the tank be filled?
- A.
7 hours
- B.
8 hours
- C.
7.5 hours
- D.
6 hours
Show answer & explanation
Correct answer: C
Concept: When two or more pipes act on the same tank at once, their effects combine: a filling pipe contributes a positive rate (fraction of the tank filled per hour) and an emptying pipe contributes a negative rate. The time to fill the tank is the reciprocal of this net combined rate: Time = 1 divided by Net Rate.
Pipe A fills the tank in 10 hours, so its rate is 1/10 tank per hour.
Pipe B fills the tank in 12 hours, so its rate is 1/12 tank per hour.
Pipe C empties the full tank in 20 hours, so its rate is -1/20 tank per hour.
Net rate = 1/10 + 1/12 - 1/20. Using the LCM of 10, 12 and 20, which is 60: = 6/60 + 5/60 - 3/60 = 8/60 = 2/15 tank per hour.
Time to fill the tank = 1 divided by (2/15) = 15/2 = 7.5 hours.
Cross-check: In 7.5 hours, Pipe A fills 7.5/10 = 0.75 of the tank, Pipe B fills 7.5/12 = 0.625 of the tank, and Pipe C empties 7.5/20 = 0.375 of the tank. Net filled fraction = 0.75 + 0.625 - 0.375 = 1.0, i.e. the whole tank -- confirming 7.5 hours is correct.