Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 3 of Exercise 10E
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
3
The sum of two natural numbers is 28 and their product is 192. Find the numbers.
Let the required number be x and 28 – x
According to given condition,
x(28 – x) = 192
x2 – 28x + 192 = 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 = 1 b = – 28 c = 192
= 1.192 = 192
And either of their sum or difference = b
= – 28
Thus the two terms are – 16 and – 12
Sum = – 16 – 12 = – 28
Product = – 16. – 12 = 192
x2 – 28x + 192 = 0
x2 – 16x – 12x + 192 = 0
x(x – 16) – 12(x – 16) = 0
(x – 16) (x – 12) = 0
(x – 16) = 0 or (x – 12) = 0
x = 16 or x = 12
Hence the required numbers are 16, 12
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.
