Q31 of 49 Page 1

Two pipes running together can fill a cistern in minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.

Let the time taken by quicker pipe = x minutes

Then the time taken by slower pipe =(x + 3) minutes


Given that two pipes together fill cistern in minutes.


So,



40(2x + 3)=13x(x + 3)


80x + 120=13x2 + 39x


13x2-41x-120=0


13x2-65x + 24x-120=0


13x(x-5) + 24(x-5)=0


(13x + 24)(x-5)=0


There are two solutions possible: or x=5


As time cannot be a negative value, x=5 minutes.


Time taken by quicker pipe = 5minutes


Time taken by slower pipe = 8minutes


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