Multiple choice

Time taken by two pipes A and B to fill a cistern is 28 hours and 32 hours, respectively. At a particular instant of time, we open both pipes to fill the cistern. There is a little hole at the bottom of the cistern. The pipes took 64 minutes more. After completely filling the cistern, how much time would the hole take to empty the cistern?

  1. 112 hours

  2. 224 hours

  3. 118 hours

  4. 236 hours

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

Rate A = 1/28, Rate B = 1/32. Combined rate = 1/28 + 1/32 = (8+7)/224 = 15/224. Time = 224/15 hours = 14.933 hours = 896 minutes. With hole, time = 896 + 64 = 960 minutes = 16 hours. Combined rate - hole = 1/16. Hole rate = 15/224 - 1/16 = (15-14)/224 = 1/224. Hole takes 224 hours.

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