Concept of “Pipes and Cistern”-02

Question: A pipe can empty a tank in 9 hours and another pipe can empty it in 6 hours. If both the pipes are opened simultaneously, find the time in which a full tank is emptied.  [Ans. (e) none of these (3.6 hours)] 

(a) 3 hours  (b) 3.5 hours  (c) 4.6 hours  (d) 15 hours  (e) none of these

Solution:

Detailed Explanation:

Concept: If an outlet pipe A can make a tank empty in “x” hours and another outlet pipe B can make the same tank empty “y” hours, then both the outlet pipes together can make the whole tank empty in xy/(x+y) hours.

First Method: Given that two pipes can make a tank empty in 9 hours and 6 hours respectively, so both together can make the tank empty in   

(9×6)/(9+6) = (9×6)/(15) = 3.6 hours Ans.

Second Method: Since the two pipes can make a tank empty in 9 hours and 6 hours respectively, so the parts of the tank to be emptied by them in one hour are respectively 1/9 and 1/6.

The total part emptied by both the pipes together in one hour is 1/9+1/6 = 5/(18).

Therefore, the whole tank will be emptied by the two pipes together in 3.6 hour. Ans.