Concept of “Pipes and Cistern”-03

Question: A pipe can fill a tank in 10 hours and another pipe can empty it in 12 hours. If both the pipes are opened, find the time in which tank is filled. [एक पाइप किसी टंकी को 10 घंटे में भर सकता है, जबकि दूसरा उसे 12 घंटे में खाली कर सकता है. यदि दोनों पाइप एक साथ खोल दिए जायें, तो बताइए कि टंकी कितनी देर में भार जाएगी?]   [Ans. (d) 60 hours ]

(a) 30 hours  (b) 80 hours  (c) 75 hours  (d) 60 hours (e) none of these

Solution: 

Detailed Explanation:

Concept: “If an inlet pipe A can fill a tank in “x” hours and an outlet pipe B can make the tank empty in “y” hours; then if both the pipes are opened together, then the tank will be filled or emptied in xy/(y-x) hours.”

First Method: Given that a pipe can fill a tank in 10 hours and another pipe can empty it in 12 hours, so both together can fill the tank in   

(10×12)/(12-10) = (10×12)/(2) = 60 hours Ans.

Second Method: Since a pipe can fill a tank in 10 hours and another pipe can empty it in 12 hours respectively, so the parts of the tank filled and emptied by them in one hour are respectively 1/10 and 1/12.

The total part filled by both the two pipes in one hour is 1/10-1/12 = 6-5/(60) = 1/60.

Therefore, the whole tank will be filled by the two pipes together in 60 hour. Ans.