Question

The denominator of a fraction exceeds its numerator by $5$. If $2$ is added to both numerator and the denominator, the fraction becomes $\frac{4}{5}.$ Find the fraction.

Answer 1

The denominator of a fraction exceeds its numerator by $5$.

$d=n+5$ $............\left(1\right)$

According to the question,

$\frac{n+2}{d+2}=\frac{4}{5}$

$5n+10=4d+8$

$5n=4d-2$

$5n=4(n+5)-2$ $Fromequation\left(1\right)$

$5n=4n+20-2$

$n=18$

$d=23$

Therefore, fraction will be

$\frac{n}{d}=\frac{18}{23}$