Question

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, 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? 

(a) 96 hours 

(b) 102 hours 

(c) 106 hours 

(d) 112 hours

Answer 1

(d) 112 hours

Part of the cistern filled by the two pipes in 1 hour = \(\big(\frac{1}{14}+\frac{1}{16}\big)\) = \(\frac{15}{112}\)

\(\therefore\) Total time taken by the two pipes and the leak to fill up the cistern = \(\big(\frac{112}{15}+\frac{32}{60}\big)\) hrs.

\(\therefore\) Part of the cistern emptied by the leak in 1 hour 

= \(\big(\frac{1}{8}-\frac{15}{112}\big)\) = \(\frac{16-15}{112}\) = \(\frac{1}{112}\)

\(\therefore\) The leak will empty the cistern in 112 hours.