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

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

Let the required fraction be x. Then 1 - x = 9 x 20 ∴ 1 - x2 = 9 x 20 ⟹ 20 - 20x2 = 9x ⟹ 20x2 + 9x - 20 = 0 ⟹ 20x2 + 25x - 16x - 20 = 0 ⟹ 5x(4x + 5) - 4(4x + 5) = 0 ⟹ (4x + 5)(5x - 4) = 0 x = 4 5

3⁄5
3⁄10
4⁄5
4⁄3

Correct Answer: 4⁄5

Explanation:

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

∴	1 - x²	=	9
	x		20

⟹ 20 - 20x² = 9x

⟹ 20x² + 9x - 20 = 0

⟹ 20x² + 25x - 16x - 20 = 0

⟹ 5x(4x + 5) - 4(4x + 5) = 0

⟹ (4x + 5)(5x - 4) = 0

x =	4
	5

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