Multiple choice

Pipe P can fill a tank in 15 minutes, while pipe Q can fill the same tank in 30 minutes. Another pipe R can empty the tank in 20 minutes. In how many minutes will the tank be full if all the three pipes are opened together and after 10 minutes, pipe R is closed?

  1. 10 minutes

  2. 12 minutes

  3. 15 minutes

  4. 21 minutes

  5. 23 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P rate = 1/15, Q rate = 1/30, R rate = -1/20. Combined rate (P+Q+R) = (4+2-3)/60 = 3/60 = 1/20. In 10 minutes, they fill 10/20 = 1/2 of the tank. Remaining 1/2 is filled by P+Q at rate (1/15 + 1/30) = 3/30 = 1/10. Time = (1/2) / (1/10) = 5 minutes. Total time = 10 + 5 = 15 minutes.

AI explanation

Let the total capacity of the tank be the least common multiple of 15, 30 and 20, which is 60 units. The filling rates of pipes P and Q are 4 units per minute and 2 units per minute, while the emptying rate of pipe R is 3 units per minute. When all three pipes are open, their net rate is 4 plus 2 minus 3, which equals 3 units per minute. In the first 10 minutes, they fill 30 units, leaving 30 units unfilled. After pipe R is closed, pipes P and Q fill at a combined rate of 6 units per minute, so they take 30 divided by 6, or 5 minutes to finish. The total time is 10 plus 5, resulting in 15 minutes.

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