Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 14 of Exercise 10E
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
The difference of two natural numbers is 3 and the difference of their 3 reciprocals is 3/28.Find the numbers.
Let the required natural numbers x and (x + 3)
x < x + 3
Thus 
According to given condition,
taking LCM
cross multiplying
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 = 3 c = – 28
= 1. – 28 = – 28
And either of their sum or difference = b
= 3
Thus the two terms are 7 and – 4
Difference = 7 – 4 = 3
Product = 7. – 4 = – 28
x(x + 7) – 4(x + 7) = 0
(x – 4) (x + 7) = 0
(x – 4) = 0 or (x + 7) = 0
x = 4 or x = – 7
x = 4 (x < x + 3)
x + 3 = 4 + 3 = 7
Hence required numbers are 4 and 7.
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.
