CAT 2015 Quantitative Ability

3x + y + 4 = 2x y
⇒ 3x + 4 = y (2x - 1)
$\Rightarrow \mathit{y}=\frac{\left(3\mathit{x}+4\right)}{\left(2\mathit{x}-1\right)}$
When x = 6⇒ y = 2
When x = 1⇒ y = 7
These two are the only possible pairs of values of x and y. Where x and y are natural numbers
∴ Required ratio = $\frac{\left(6+1\right)}{\left(2+7\right)}=\frac{7}{9}$