The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is  Choose the correct choice from the following:
A) 4 / 5  B) 7 / 11  C) 7 / 13  D) 7 / 15  E) 8 / 11

Rationale: 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 a )
Answer: A