Question

The sum of the numerator and denominator of a fraction is $4$ more than twice the numerator. If the numerator and denominator are increased by $3$, they are in the ratio $2:3$. Determine the fraction.

Answer 1

Let the fraction $=\frac{x}{y}$

First condition :

$\Rightarrow x+y=4+2\left(x\right)$

$\Rightarrow -x+y=4$

Second condition :

$\Rightarrow \frac{x+3}{y+3}=\frac{2}{3}$

$\Rightarrow 3x+9=2y+6$

$\Rightarrow 3x-2y=-3$

$\Rightarrow x=5$

$\Rightarrow y=9$

$\Rightarrow$fraction $=\frac{5}{9}$