Maths - Pipe & Cisterns

Concept of “Pipes and Cistern”-01
Question: Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? [दो पाइप A तथा B एक टंकी को क्रमशः 36 घंटे और 45 घंटे में भर सकते हैं. यदि दोनों पाइप एक साथ खोल दिए जायें, तो कितने समय में वह टंकी भर जाएगी?]  [Ans. (d) 20 hours]          
(a) 30 hours  (b) 24 hours  (c) 25 hours  (d) 20 hours  (e) None of these

Solution:

Detailed Explanation:
Concept:

(1) If an inlet pipe A can fill a tank in “x” hours and another inlet pipe B can fill the same tank “y” hours, then both the inlet pipes together can fill the whole tank in xy/(x+y) hours.

(2) 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.

(3) If an inlet pipe A can fill a tank in “x” hours, another inlet pipe B can fill the tank in “y” hours and a third inlet pipe C can fill the same tank “z” hours, then all the three inlet pipes together can fill the whole tank in 1/(1/x+1/y+1/z) hours or, xyz/(xy+yz+zx) hours.

(4) If an outlet pipe A can make a tank empty in “x” hours, another outlet pipe B can make the tank empty in “y” hours and a third outlet pipe C can make the same tank empty in “z” hours, then all the three outlet pipes together can make the whole tank empty in 1/(1/x+1/y+1/z) hours or, xyz/(xy+yz+zx) hours.

(5) 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 two pipes A and B can fill a tank in 36 hours and 45 hours respectively, so both together can fill the tank in  
(36×45)/(36+45) = (36×45)/(81) = 20 hours Ans.

Second Method: Since two pipes A and B can fill a tank in 36 hours and 45 hours respectively, so the parts of the tank filled by them in one hour are respectively 1/36 and 1/45.
The total part filled by both the pipes A and B together in one hour is 1/36+1/45 = 81/(36 ×45) = 1/20.

Therefore, the whole tank will be filled by the pipes A and B together in 20 hour. Ans.