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 $\frac{3}{2}$. Find the rational number.

Answer 1

let the numerator of a rational number be x, then the denominator is x+8.
Therefore, Rational number $=\frac{x}{x+8}$
According to question,
$\frac{x+17}{x+8-1}=\frac{3}{2}$
$\Rightarrow \frac{x+17}{x+7}=\frac{3}{2}$
$\Rightarrow 2(x+17)=3(x+7)$
$\Rightarrow 2x+34=3x+21$
$\Rightarrow 2x-3x=21-34$
$\Rightarrow -x=-13$ $\Rightarrow x=13$

Hence, the required rational number
$\frac{x}{x+8}=\frac{13}{13+8}=\frac{13}{21}$