Pipes and Cisterns

Pipes and Cisterns

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.

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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 :

            

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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 :

            

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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 :

            

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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 :

     

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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

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Ex. A cistern is normally filled in 8 hrs, but it takes four hrs longer to fill because 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 completely filled in 8x / x - 8

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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 remaining = 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.