Multiple choice

A cistern can be filled by pipes A and B in 4 hours and 6 hours, respectively. When full, the cistern can be emptied by a pipe C in 8 hours. If all the taps are turned on at the same time, the cistern will be full in

  1. 3 hours 18 minutes

  2. 3 hours 26 minutes

  3. 3 hours 42 minutes

  4. 3 hours 48 minutes

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The rates are A=1/4, B=1/6, and C=-1/8. Combined rate = 1/4 + 1/6 - 1/8 = (6+4-3)/24 = 7/24. Time to fill = 24/7 hours, which is 3 hours and 3/7 hours. 3/7 of 60 minutes is approximately 25.7 minutes.

AI explanation

Using the LCM method, assume the total capacity of the cistern is 24 units. The respective rates for A, B, and C are 6 units per hour, 4 units per hour, and 3 units per hour. The net rate when all three are open is 7 units per hour, meaning the cistern fills in 24 divided by 7 hours. Converting this improper fraction gives 3 hours and (3 divided by 7) times 60 minutes, which is 3 hours 26 minutes.

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