Basics of Pipes and Cisterns:
Problems based on this topic is asked every year in SSC CGL,CHSLE,state SSC,Banking,ibps and other competitive exams.So it becomes necessary for us to learn this topic in depth.So let us Learn it.
Inlet : A pipe connected with a tank or reservoir for filling is called as inlet
Outlet : A pipe connected with a tank and used for empties it is called outlet.
Rule : If a pipe can fill a tank in x hours, then the part filled in 1 hour = 1 / x
Rule : If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then the net part filled in 1 hour, when both the pipes are opened :
Time taken to fill the tank, when both the pipes are opened :
Rule : If a pipe can fill a tank in x hours and another fill the same tank in y hours, then the net part filled in 1 hr, when both pipes are opened:
So time to fill the tank will be :
Rule: If a pipe fills a tank in x hrs and another fills the same tank in y hrs, but a third empties the full tank in z hrs and all of them are opened together, the net part filled in 1 hr :
So time taken to fill the tank :
Ex. A tank is filled by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank ?
Solution : Let Pipe A take x hours to fill the tank , then pipes B will take x / 2 hrs and pipe C will take x / 4 hours respectively.
Then part to be filled by all three pipes in 1 hrs will be :
Ex. Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B can fill the remaning part in 7 hours. Find the number of hours taken by C alone to fill the tank .
Solution : Work done by A+B+C in 2 hours = 2 /6 = 1 / 3
So, work remaning = 1- ( 1/ 3 ) = 2 / 3
Now (A + B)'s 7 hour work = 2 / 3
( A + B )'s 1 hour work will be = 2 / 21
So C's 1 hour work will be = 1 hour work of (A+B+C) - 1 hour work of (A+B) = ( 1/ 6) - ( 2/ 21) = 1 / 14
So C alone can fill the tank in 14 hours
Ex. A cistern is normally filled in 8 hrs, but it takes four hrs longer to fill beacuse of a leak in the bottom. If the cistern is full , how much time the leak will empty it ?
Solution : Let the leak will empty the tank in x hrs.
Then part of cistern filled in 1 hr = ( 1 / 8 ) - ( 1 / x ) = x - 8 / 8x
So cistern will completly filled in 8x / x - 8
Ex. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, Pipe A is turned off. What is the total time required to fill the tank ?
Solution :Part of tank filled by A + B in 1 minute = ( 1 / 15 + 1 / 20 )
So tank filled by A + B in 4 minute = 4 ( 1 / 15 + 1 / 20 ) = 7 / 15
Part remaning = 1 - ( 7 / 15 ) = 8 / 15
1 / 20 part is filled by B in 1 minute
So, 8 / 15 part will be filled in = ( 20 / 1 )* ( 8 / 15 ) = 32 / 3 = 10 minutes 40 sec.
For More Practice:
Practice Test I CLICK HERE!!
Practice Test II CLICK HERE!!
Basics of Pipes and Cisterns CLICK HERE!!
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