 ## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 21 of Exercise 10E

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

21
##### Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

Let the two natural numbers be x and y.

According to the question

x2 + y2 = 25(x + y) – – – – – (1)

x2 + y2 = 50(x – y) – – – – (2)

From (1) and (2) we get

25(x + y) = 50(x – y)

x + y = 2(x – y)

x + y = 2x – 2y

y + 2y = 2x – x

3y = x – – – – – (3)

From (2) and (3) we get

(3y)2 + y2 = 50(3y – y)

9y2 + y2 = 50(3y – y)

10 y2 = 100y

y = 10

From (3) we have,

x = 3y = 3.10 = 30

Hence the two natural numbers are 30 and 10.

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

## Students Store ##### Stationery Store ##### Lunch Boxes ##### Hair Accessories ##### Sippers & Bottles 