Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it tooki 32 minutes more to fill the cistern.When the cistern is full, in what time will the leak empty it?
100 hrs
122 hrs
177 hrs
112 hrs
Correct Answer :
D. 112 hrs
Work done by the two pipes in 1 hour =(1/14)+(1/16)=(15/112).
Time taken by these pipes to fill the tank = (112/15) hrs = 7 hrs 28 min.
Due to leakage, time taken = 7 hrs 28 min + 32 min = 8 hrs
Work done by (two pipes + leak) in 1 hour = (1/8).
Work done by the leak m 1 hour =(15/112)-(1/8)=(1/112).
Leak will empty the full cistern in 112 hours.