If $$\frac{a}{3} = \frac{b}{2}{\text{,}}$$   then the value of $$\frac{{2a + 3b}}{{3a - 2b}}\,{\text{is?}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{a}{3} = \frac{b}{2} \Rightarrow \frac{a}{b} = \frac{3}{2} \cr & \therefore \frac{{2a + 3b}}{{3a - 2b}} \cr & = \frac{{2 \times 3 + 3 \times 2}}{{3 \times 3 - 2 \times 2}} \cr & = \frac{{6 + 6}}{{9 - 4}} \cr & = \frac{{12}}{5} \cr} $$