# 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.

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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