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, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ?
Select.
A) 110 hours  B) 112 hours  C) 115 hours  D) 100 hours  E) None of these
Cistern filled by both pipes in one hour   = 1⁄14 + 1⁄16 = 15⁄112th   ∴ Both pipes filled the cistern in 112⁄15 hrs.   Now, due to leakage both pipes filled the cistern in   112⁄15 + 32⁄60 = 8 hrs.   ∴ due to leakage, filled part in one hour 1⁄8   ∴ part of cistern emptied, due to leakage in one hour   = 15⁄112 - 1⁄8 = 1⁄112th   ∴ in 112 hr, the leakage would empty the cistern.   Answer 112 hours
<result>B</result>
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, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ?