Q. 483.7( 9 Votes )

Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

Answer :

Let the first pipe fill the cistern in ‘X’ minutes, then the second pipe requires ‘(X+5)’ minutes to fill it.


Applying the concept of Unitary Method,


In one minute, both pipes will fill the part of cistern as below:





12X + 30 = X2 + 5X


X2 – 7X – 30 = 0


On factorising the same.


X2 – 10X + 3X – 30 = 0


X(X – 10) + 3(X – 10) = 0


(X – 10)(X + 3) = 0


X = – 3 or X = 10.


Then the first pipe will fill the cistern in ‘X’ minutes i.e., 10 minutes and the second pipe will fill the cistern in ‘(X+5)’ minutes i.e., 15 minutes.


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