Two pipes can fill a cistern in 8 hours and 7 hours respectively The pipes are opened simultaneously...........

Quantitative Aptitude ( CCS) Pipes&cistern

Two pipes can fill a cistern in 8 hours and 7 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 16 minutes more to fill the cistern. When the cistern is full, in what time the leak empty it ?

28 hours

56 hours

72 hours

84 hours

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Explanation:

Work done by the two pipes in 1 hour = (1/8 + 1/7) = 15/56.
.'. Time taken by these pipes to fill the tank = 56/15 hrs = 3 hrs 44 min.
Due to leakage, time taken = 3 hrs 44 min + 16 min. = 4 hours.
.'. Work done by (two pipes + leak) in 1 hour = 1/4.
Work done by the leak in 1 hour = (15/56 - 1/4) = (15 - 14)/56 = 1/56.
.'. Leak will empty the full cistern in 56 hours.