Multiple choice

Two pipes A and B can fill a tank in 15 hours and 20 hours, respectively. The third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. In how much time will the tank be full?

  1. 2 hours

  2. 3 hours 30 minutes

  3. 2 hours 30 minutes

  4. 1 hour

  5. 3 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rates: A=1/15, B=1/20, C=-1/25. Combined rate = 1/15 + 1/20 - 1/25 = (20+15-12)/300 = 23/300. In 10 hours, work done = 230/300 = 23/30. Remaining = 7/30. After C closes, rate = 1/15 + 1/20 = 7/60. Time = (7/30) / (7/60) = 2 hours.

AI explanation

Using the net work method, the rates of pipes A, B, and C are 1/15, 1/20, and -1/25 respectively, making their combined rate (20 + 15 - 12)/300 = 23/300 per hour. In the first 10 hours, the three pipes together fill 10 * 23/300 = 230/300, leaving 70/300 or 7/30 of the tank unfilled. After pipe C is closed, the net filling rate of pipes A and B becomes 1/15 + 1/20 = 7/60 per hour. The time needed to fill the remaining 7/30 of the tank at this new rate is (7/30) / (7/60) = 2 hours.

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