Question

The numerator of a fraction is four less than its denominator. If $1$ is added to both, its numerator and denominator, the fraction becomes $\frac{1}{2}$. Find the fraction.

Answer 1

Let the denominator be $x$.

$\therefore$ Numerator of the fraction $=x-4$

Therefore the fraction is $\frac{x-4}{x}$

Given that if $1$ is added to both, its numerator and denominator, the fraction becomes $\frac{1}{2}$, i.e.,

$\frac{(x-4)+1}{x+1}=\frac{1}{2}$

$\frac{x-4+1}{x+1}=\frac{1}{2}$

$2(x-3)=x+1$

$2x-6=x+1$

$2x-x=6+1\Rightarrow x=7$

Hence the fraction is $\frac{7-4}{9}=\frac{3}{9}$

Hence the correct answer is $\frac{1}{3}$.