Discussion
Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?
Answer: B
Time taken by two pipes to fill the tank = \(1/14 + 1/16 = (8+7)/112 = 15/112\). So they take 112/15 hours. Due to leakage, time taken = \(112/15 + 32/60 = 112/15 + 8/15 = 120/15 = 8\) hours. Let the leak empty the tank in x hours. So, \(1/14 + 1/16 - 1/x = 1/8 \Rightarrow 15/112 - 1/x = 1/8 \Rightarrow 1/x = 15/112 - 1/8 = (15-14)/112 = 1/112\). So, x = 112 hours.
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