Multiple choice

Two pipes A and B can fill a tank in 10 hr each, while a third pipe C can empty the tank in 8 hr. At 9 a.m, pipe A is opened and at 11 a.m, the other two pipes are opened. At what time will the tank be full?

  1. Between 6 p.m. and 7 p.m.

  2. Between 10 p.m. and 11 p.m.

  3. Between 9 p.m. and 10 p.m.

  4. Between 8 p.m. and 9 p.m.

  5. Between 7 p.m. and 8 p.m.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A fills 1/10 per hour. B fills 1/10 per hour. C empties 1/8 per hour. From 9 to 11, A fills 2/10 = 1/5. Remaining = 4/5. From 11 onwards, net rate = 1/10 + 1/10 - 1/8 = 2/10 - 1/8 = 1/5 - 1/8 = 3/40. Time to fill remaining = (4/5) / (3/40) = (4/5) * (40/3) = 32/3 = 10 hours 40 minutes. 11 a.m. + 10 hours 40 minutes = 9:40 p.m.

AI explanation

Using the one-day work method, pipe A works alone for 2 hours at a rate of 1/10 per hour to fill 2/10 or 1/5 of the tank, leaving 4/5 of the tank unfilled. When pipes B and C open at 11 a.m., the net hourly rate becomes 1/10 + 1/10 - 1/8 = 3/40. The time needed to fill the remaining 4/5 of the tank at this net rate is (4/5) / (3/40) = 32/3 hours, or 10 hours and 40 minutes. Adding this duration to 11 a.m. results in a completion time of 9:40 p.m., which falls between 9 p.m. and 10 p.m.

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