# 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,

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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.

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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