Multiple choice

A cistern has two inlets A and B which can be filled in 12 minutes and 15 minutes, respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty cistern, then the time taken to fill the cistern completely is__________.

  1. 20 minutes

  2. 10 minutes

  3. 15 minutes

  4. 5 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rates of the inlets A and B are 1/12 and 1/15 of the cistern per minute, respectively, while the outlet C empties at a rate of 1/10 per minute. When all three are opened together, the net rate of filling per minute is 1/12 + 1/15 - 1/10 = 3/60 = 1/20. Therefore, it will take 20 minutes to fill the cistern completely.

AI explanation

Using the LCM method, let the total capacity of the cistern be the least common multiple of 12, 15, and 10, which is 60 units. The filling rates of inlets A and B are 5 units per minute and 4 units per minute respectively, while outlet C empties at 6 units per minute. When all three pipes are opened together, the effective filling rate is 5 plus 4 minus 6, equaling 3 units per minute. The total time taken to fill the 60 unit cistern at this rate is 60 divided by 3, resulting in 20 minutes.

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