Multiple choice

Two inlet pipes, A and B, can fill a cistern in 12 hours and 15 hours respectively. A third pipe, C, is an outlet pipe that can empty the cistern in 20 hours. All three pipes are opened together, but after 4 hours, pipe C is closed and another outlet pipe, D, which can empty the cistern in 30 hours, is opened instead. If the cistern was empty at the start, in how much total time will it be completely filled? (approximately in hours)

  1. 7

  2. 9

  3. 12

  4. 15

  5. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rates (per hour): A=1/12, B=1/15, C=-1/20. Combined rate = 1/12 + 1/15 - 1/20 = (5+4-3)/60 = 6/60 = 1/10. In 4 hours, they fill 4/10 = 2/5 of the cistern. Remaining = 3/5. New rate (C replaced by D): A+B-D = 1/12 + 1/15 - 1/30 = (5+4-2)/60 = 7/60. Time to fill remaining = (3/5) / (7/60) = (3/5) * (60/7) = 36/7 approx 5.14 hours. Total time = 4 + 5.14 = 9.14 hours.

AI explanation

Using the LCM method, assume the cistern capacity is 60 units, making the rates for pipes A, B, C, and D equal to 5, 4, -3, and -2 units per hour respectively. In the first 4 hours, all three pipes work together to fill (5 + 4 - 3) * 4 = 24 units. For the remaining 36 units, pipe C is replaced by pipe D, making the new combined rate 5 + 4 - 2 = 7 units per hour, which takes 36/7 hours. The total time is 4 + 36/7, which equals 64/7 hours, or approximately 9 hours.

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