Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 56 of Exercise 10E
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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.
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
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.
