Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 13 of Exercise 10E
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The sum of two natural numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers.
Let the required natural numbers x and (15 – x)
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 = – 15 c = 50
= 1.50 = 50
And either of their sum or difference = b
= – 15
Thus the two terms are – 10 and – 5
Sum = – 10 – 5 = – 15
Product = – 10. – 5 = 50
x(x – 10) – 5(x – 10) = 0
(x – 5) (x – 10) = 0
(x – 5) = 0 or (x – 10) = 0
x = 5 or x = 10
Case I: when x = 5
15 – x = 15 – 5 = 10
Case II: when x = 10
15 – x = 15 – 10 = 5
Hence required numbers are 5 and 10.
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.
