## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 19 of Exercise 10E

Listen NCERT Audio Books - Kitabein Ab Bolengi

19
##### Divide 27 into two parts such that the sum of their reciprocals is 3/20.

Let the two parts be x and (27 – x)

According to given condition,

On taking the LCM

On 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 = – 27 c = 180

= 1. – 180 = – 180

And either of their sum or difference = b

= – 27

Thus the two terms are – 15 and – 12

Sum = – 15 – 12 = – 27

Product = – 15. – 12 = 180

x (x – 15) – 12(x – 15) = 0

(x – 15) (x – 12) = 0

(x – 15) = 0 or (x – 12) = 0

x = 15 or x = 12

Case I: when x = 12

27 – x = 27 – 12 = 15

Case II: when x = 15

27 – x = 27 – 15 = 12

Hence required numbers are 12 and 15.

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