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?

A) \( \Large 43\frac{19}{23} \) h
B) \( \Large 43\frac{17}{23} \) h

C) \( \Large 43\frac{13}{23} \) h
D) \( \Large 43\frac{15}{23} \) h

Correct answer:
A) \( \Large 43\frac{19}{23} \) h

Description for Correct answer:
Part filled by 2nd pipe in 1 h = \( \Large \frac{1}{14} \)

Part filled by 2nd pipe in 1 h = \( \Large \frac{1}{16} \)

Part filled by the two pipes in 1 h = \( \Large \left(\frac{1}{14}+\frac{1}{16}\right)=\frac{8+7}{112}=\frac{15}{112} \)

Therefore, Time taken by these two pipes cistern

= \( \Large \frac{112}{15} \) = 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 = \( \Large \frac{1}{9} \)

Work done by the leak in 1 h = \( \Large \frac{1}{9}-\frac{15}{112}=\frac{112-135}{1008}

= - \frac{23}{1008} \)

Therefore, Time taken by leak to empty the full cistern

= \( \Large \frac{1008}{23} = 43\frac{19}{23} \)

Please provide the error details in above question

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