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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.
Solution
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`
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