Question

The denominator of a fraction is 3 more than the numerator.If $5$ is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}.$ Find the fraction.

Answer 1

Let the numerator of a fraction be $x$.

$\Rightarrow$ Denominator of the fraction $=x+3$

$\Rightarrow$ The fraction $=\frac{x}{x+3}$

If $5$ is added to both parts, it will become as $\frac{4}{5}$.

$\Rightarrow \frac{x+5}{x+3+5}=\frac{4}{5}$

$\Rightarrow \frac{x+5}{x+8}=\frac{4}{5}$

$\Rightarrow 5x+25=4x+32$

$\Rightarrow 5x-4x=32-25$

$\Rightarrow x=7$.

Therefore, the fraction is $\frac{x}{x+3}=\frac{7}{7+3}=\frac{7}{10}$

Hence, the required fraction is $\frac{7}{10}$.