Question

The sum of a number and its reciprocal is `2 1/20`. The number is ______.

Options

• `5/4` or `4/5`

• `4/3` or `3/4`

• `5/6` or `6/5`

• `1/6` or 6

Answer 1

The sum of a number and its reciprocal is `2 1/20`. The number is `underlinebb(5/4 or 4/5)`.

Explanation: 

Let the required number be x. 

According to the question:  

`x + 1/x = 41/20` 

⇒ `(x^2 + 1)/x = 41/20` 

⇒ 20x² – 41x + 20 = 0

⇒ 20x² – 25x – 16x + 20 = 0 

⇒ 5x(4x – 5) – 4(4x – 5) = 0 

⇒ (4x – 5) (5x – 4) = 0 

⇒ `x = 5/4` or `x = 4/5`