Question

In a fraction, twice the numerator is $2$ more than the denominator.If $3$ is added to the numerator and to the denominator, the new fraction is $\frac{2}{3}$.Find the original fraction.

Answer 1

Let the numerator be $x$

Denominator $=2x-2$

Therefore the fraction $=\frac{x}{2x-2}$

Given: when $3$ is added to both the numerator and denominator, the fraction becomes $\frac{2}{3}$.

Hence $\frac{(x+3)}{(2x-2+3)}=\frac{2}{3}$

$\frac{(x+3)}{(2x+1)}=\frac{2}{3}$

$\Rightarrow 3x+9=4x+2$

$\Rightarrow x=7$

$\therefore$ the fraction is $\frac{7}{12}$.