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Q1: 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

ANS:C -

4
5

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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