Question

When $3$ is added to the denominator and $2$ is subtracted from the numerator a fraction becomes $\frac{1}{4}$. And, when $6$ is added to numerator and the denominator is multiplied by $3$, it becomes $\frac{2}{3}$. Find the fraction.

Answer 1

Let the numerator be $x$ and denominator be $y$

$\Rightarrow Nowbyfirstcondition\frac{x-2}{y+3}=\frac{1}{4}$.

$\Rightarrow 4(x-2)=(y+3)$

$\Rightarrow 4x-8=y+3=>4x-y=11$........................1

And By second condition $\frac{x+6}{3y}=\frac{2}{3}$

$\Rightarrow 3(x+6)=6y$

$\Rightarrow 3x-6y=-18$............................................2

$6\left(1\right)-\left(2\right)$

$21x=84$

$x=4$

$by1y=5$