If $$\frac{x}{y} = \frac{3}{4}{\text{,}}$$  the ratio of (2x + 3y) and (3y - 2x) is = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given }} \cr & \frac{x}{y} = \frac{3}{4} \cr & \Rightarrow \frac{{2x + 3y}}{{3y - 2x}} \cr & = \frac{{2 \times 3 + 3 \times 4}}{{3 \times 4 - 2 \times 3}} \cr & = \frac{{6 + 12}}{{12 - 6}} \cr & = \frac{{18}}{6} \cr & = 3:1 \cr} $$
This is the required ratio 3 : 1