Lessons

General Aptitude
9.1 Numbers - General Questions

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Q.

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

View Answer

Correct choice: C

Explanation:

Let the required fraction be x. Then (1/x) - x = 9/20
∴(1 - x2 )/x = 9/20

⇒  20 - 20x2 = 9x

  ⇒   20x2 + 9x - 20 = 0

  ⇒   20x2 + 25x - 16x - 20 = 0

  ⇒   5x(4x + 5) - 4(4x + 5) = 0

  ⇒   (4x + 5)(5x - 4) = 0

  ⇒   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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