If $$\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = 3,$$    then $$\frac{{2{a^2} + 3{c^2} + 4{e^2}}}{{2{b^2} + 3{d^2} + 4{f^2}}}$$    = ?

Solution (By Examveda Team)

$$\eqalign{ & \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{3}{1} \cr & \Rightarrow \frac{{2 \times 9 + 3 \times 9 + 4 \times 9}}{{2 \times 1 + 3 \times 1 + 4 \times 1}} \cr & \Rightarrow \frac{{18 + 27 + 36}}{{2 + 3 + 4}} \cr & \Rightarrow \frac{{81}}{9} \cr & \Rightarrow 9 \cr} $$