## Book: RS Aggarwal - Mathematics

### Chapter: 10. Quadratic Equations

#### Subject: Maths - Class 10th

##### Q. No. 40 of Exercise 10E

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

40
##### The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.

Let the present age of boy and his brother be x years and (25 – x) years

According to given question

x(25 – x) = 126

25x – x2 = 126

x2 – 25x + 126 = 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 = – 25 c = 126

= 1.126 = 126

And either of their sum or difference = b

= – 25

Thus the two terms are – 18 and – 7

Sum = – 18 – 7 = – 25

Product = – 18. – 7 = 126

x2 – 18x – 7x + 126 = 0

x (x – 18) – 7(x – 18) = 0

(x – 18) (x – 7) = 0

x = 18 or x = 7

x = 18 (Present age of boy cannot be less than his brother)

if x = 18

The present age of boy is 18 years and his brother is (25 – 18) = 7years

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71