# The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is increased by 1, th

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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 increased by 1, the number becomes 3/2. Find the rational number.
1. 7/15
2. 5/13
3. 3/11
4. 9/17

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Correct Answer - Option 1 : 7/15

Given:

The denominator of a rational number is greater than its numerator by 8.

Calculation:

Let the numerator of a rational number be x and denominator be (x + 8).

ATQ,

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

⇒ (x + 17)/(x + 9) = 3/2

⇒ 2x + 34 = 3x + 27

⇒ x = 7 and x + 8 = 7 + 8 = 15

⇒ Rational number = 7/15

∴ The required rational number is 7/15.