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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.

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. 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Let the numerator be x then denominator will be (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
The rational number is x/(x + 8) = 13/21

Thanks

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