Question

The denominator of a rational number is greater than its numerator by $3$. If $3$ is subtracted from numerator $2$ is added to its denominator the new no. becomes $\frac{1}{5}$, Find original number.

Answer 1

Let the required number be $\frac{x}{y}$.

Since denominator of the number is greater than its numerator by $3$.

$\therefore y=x+3.....\left(1\right)$

Also,

$\frac{x-3}{y+2}=\frac{1}{5}$

$5(x-3)=y+2$

$5x-15=(x+3)+2$

$5x-15=x+5$

$5x-x=15+5$

$\Rightarrow x=\frac{20}{4}=5$

Substituting the value of $x$ in equation $\left(1\right)$, we have

$y=5+3=8$

Therefore,

Required no. $=\frac{5}{8}$