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The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2. Find the fraction.

The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2. Find the fraction.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
11 months ago
Dear student


Let numerator of a fraction be x.

Denominator = ( x + 8 )

Fraction = Numerator/Denominator = 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

3x – 2x = 34 – 21

x = 13

Numerator = x = 13

And

Denominator = X + 8 = 13+8 = 21

Thus, Fraction = 13/21


Thanks

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