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 nuber obtained is 3/2 find the rational number​

Answer 1

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Answer 2

Given

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 out

Find the rational number

Solution

★Let the numerator be x

✞Denominator of a rational number is greater than its numerator by 8

• Denominator = (x + 8)

✞Numerator is increased by 17 and the denominator is decreased by 1 the number obtained is 3/2 .

$\implies\sf \dfrac{x + 17}{(x + 8)- 1} =\dfrac{3}{2} \\ \\ \\ \implies\sf \dfrac{ x + 17}{x + 7}=\dfrac{3}{2} \\ \\ \\ \implies\sf 2(x+17)=3(x + 7) \\ \\ \\ \implies\sf 2x + 34=3x+21 \\ \\ \\ \implies\sf 34-21=3x-2x \\ \\ \\ \implies\sf x=13$

Hence,

• Required rational number

$\implies\sf \dfrac{Numerator}{denominator} \\ \\ \\ \implies\sf \dfrac{ x}{x + 8} \\ \\ \\ \implies\sf \dfrac{13}{13 + 8} \\ \\ \\ \implies\sf \dfrac{ 13}{21}$

$\rule{200}3$