Question

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is `3/2` . Find the rational number.

Answer 1

Let the numerator of the rational number be x. Therefore, its denominator will be x + 8.

The rational number will be `x/x+8` According to the question,

`(x + 17)/(x + 8 - 1) = 3/2`

`=> (x + 17)/(x + 7) = 3/2`

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 − 21 = 3x − 2x

⇒13 = x

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = `13/21`