Bhanu Chaudhary
Poll
Professional
Asked: 2022-03-06T08:58:05+05:30

Two pipes can fill a cistern in 14 and 16 h, respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, it took 92 min more to fill the cistern. When the cistern is full, in what time will the leak empty it?

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Two pipes can fill a cistern in 14 and 16 h, respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, it took 92 min more to fill the cistern. When the cistern is full, in what time will the leak empty it?

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    1 Answer

    1. Professional

      Correct Answer: 43 19/23 h

      Part filled by 2nd pipe in 1 h = 1/14

      Part filled by 2nd pipe in 1 h = 1/16

      Part filled by the two pipes in 1 h = (1/14+1/16)=8+7/112=15/112

      Therefore, Time taken by these two pipes cistern

      = 112 15 = 7 h 28 min

      Due to leakage, the time taken = 7 h 28 min + 92 min = 9 h

      Therefore, Work done by (two pipes + leak) in 1 h = 1/9

      Work done by the leak in 1 h = 1/9−15/112=112−135/1008=−23/1008

      Therefore, Time taken by leak to empty the full cistern

      = 1008/23=43 19/23

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