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 \( \frac{3}{2}\). Find the rational number.

Asked by Aaryan | 1 year ago |  221

1 Answer

Solution :-

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

The rational number will be \(\frac{x}{x + 8}\). According to the question,

⇒ 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 = \(\frac{13}{21}\)

Answered by Sakshi | 1 year ago

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