Question

The denominator of a rational number is greater than its numerator by $8$. If numerator is increased by $17$ and denominator is decreased by $1$, the number obtained is $\frac{3}{2}$. Find rational number.

Answer 1

Let numerator of rational number be $x$

$\therefore$ Denominator will be $x+8$
The rational number will be in the form of $\frac{p}{q}=\frac{x}{x+8}$
As per the question,

$\frac{x+17}{x+8-1}=\frac{3}{2}$

$\frac{x+17}{x+7}=\frac{3}{2}$
$2x+34=3x+21$

$2x-3x=21-34$
$-x=-13$
$x=13$

Numerator $\Rightarrow x=13$

Denominator $\Rightarrow x+8=13+8=21$

Rotational number $=\frac{13}{21}$