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 $32$ .The rational number is ____.

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Detailed Solution

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

32

.The rational number is

1321

.
Let x to be the numerator, then the denominator will be

x + 8

.
According to the question equation will be,

⇒ x + 17 x + 8 − 1 = 32 ⇒ 2 x + 17 = 3 x + 7 ⇒ 2 x + 2 × 17 = 3 x + 3 × 7 ⇒ 2 x + 34 = 3 x + 21

Simplifying further,

⇒ 34 − 21 = 3 x − 2 x ⇒ 13 = x ⇒ x = 13

Hence, the rational number is

1321

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