Two pipes can fill a cistern in 14 and 16 hours respectively. Both the pipes are opened simultaneously and it is found that due to leakage in the bottom \(\frac{8}{15}\) (or 32 min) hours extra had been taken to fill the tank. If the cistern is full, in what time would the leak empty the tank?
Answer & explanation
Correct answer: option 2
Time taken to fill the tank by A and B = \(\frac{112}{15}\)
Extra time taken due to leakage = \(\frac{8}{15}\)
Total time taken by A, B and Leakage = \(\frac{112}{15}\) + \(\frac{8}{15}\) = \(\frac{120}{15}\) = 8 hrs.
So,
Efficiency of A + B - Leakage = \(\frac{112}{8}\) = 14
Efficiency of Leakage = 14 - 8 - 7 = -1
Hence, leakage can empty the full tank in = \(\frac{112}{1}\) = 112 hrs.