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### Discussion :: Numbers

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

2.  A. $${3\over 5}$$ B. $${3\over 10}$$ C. $${4\over5}$$ D. $${4\over3}$$

Explanation :

Let the required fraction be x. Then$$23 (\frac { 1 } { 2 } ) 4^3$$-X=$${9\over 20}$$

$${1-X^2\over X}$$=$${9\over 20}$$

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 =$${4\over 5}$$

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