The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
[A].

3

5

[B].

3

10

[C].

4

5

[D].

4

3

Answer: Option C

Explanation:

Let the required fraction be x. Then	1	– x =	9
	x		20

	1 – x2	=	9
	x		20

     20 – 20×2 = 9x

     20×2 + 9x – 20 = 0

     20×2 + 25x – 16x – 20 = 0

     5x(4x + 5) – 4(4x + 5) = 0

     (4x + 5)(5x – 4) = 0

x =	4
	5