Multiple choice

A cistern can be filled by taps A and B in 12 minutes and 16 minutes, respectively. When the tank is full, it can be emptied by a third tap C in 8 minutes only. If all the taps are left running at the same time, then the cistern will be filled in

  1. 20 minutes

  2. 24 minutes

  3. 36 minutes

  4. 48 minutes

  5. 54 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A = 1/12, B = 1/16, C = -1/8. Combined rate = 1/12 + 1/16 - 1/8 = (4 + 3 - 6) / 48 = 1/48. The cistern fills in 48 minutes.

AI explanation

The rates of taps A, B and C are 1/12, 1/16 and minus 1/8 respectively. Adding these rates gives a common denominator of 48, resulting in 4/48 plus 3/48 minus 6/48. This equals a net rate of 1/48 of the cistern per minute. The time taken is the reciprocal of the net rate, which is 48 minutes.

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