Q. 564.0( 14 Votes )

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

Answer :

Let the time taken by one pipe to fill the tank be x minutes

The time taken by other pipe to fill the tank = x + 5 minutes


Volume of tank be V


Volume of tank filled by one pipe in x minutes = V


Volume of tank filled by one pipe in 1 minutes = V/x


Volume of tank filled by one pipe in minutes =


Volume of tank filled by other pipe in minutes =


Volume of tank filled by one pipe in minutes + Volume of tank filled by other pipe in minutes = V






200x + 500 = 9x2 + 45x


9x2 – 155x – 500 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 9 b = – 155 c = – 500


= 9. 500 = – 4500


And either of their sum or difference = b


= – 155


Thus the two terms are – 180 and 25


Difference = – 180 + 25 = – 155


Product = – 180.25 = – 4500


9x2 – 180x + 25x – 500 = 0


9x(x – 20) + 25(x – 20) = 0


(x – 20) (9x + 25) = 0


(x – 20) = 0 (9x + 25) = 0


x = 20 or x = – 25/9


x = 20 (time cannot be negative fraction)


Hence one pipe fills the tank in 20 mins. and other pipe fills the cistern in (20 + 5) = 25 mins


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