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Q1
:
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
A
4
5
B
4
3
C
3
10
D
3
5
Solution
ANS:
C
-
4
5
Let the required fraction be
x
. Then
1
-
x
=
9
x
20
1 -
x
2
=
9
x
20
20 - 20
x
2
= 9
x
20
x
2
+ 9
x
- 20 = 0
20
x
2
+ 25
x
- 16
x
- 20 = 0
5
x
(4
x
+ 5) - 4(4
x
+ 5) = 0
(4
x
+ 5)(5
x
- 4) = 0
x
=
4
5
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