The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is? Select the correct option.
A) 4/5
B) 4/7
C) 5
D) 5/7
E) None
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   Option 4/5
<result>A</result>
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is?