Question
If $$\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = 3,$$ then $$\frac{{2{a^2} + 3{c^2} + 4{e^2}}}{{2{b^2} + 3{d^2} + 4{f^2}}}$$ = ?
Answer: Option D
$$\eqalign{
& \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{3}{1} \cr
& \Rightarrow \frac{{2 \times 9 + 3 \times 9 + 4 \times 9}}{{2 \times 1 + 3 \times 1 + 4 \times 1}} \cr
& \Rightarrow \frac{{18 + 27 + 36}}{{2 + 3 + 4}} \cr
& \Rightarrow \frac{{81}}{9} \cr
& \Rightarrow 9 \cr} $$
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$$\eqalign{
& \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{3}{1} \cr
& \Rightarrow \frac{{2 \times 9 + 3 \times 9 + 4 \times 9}}{{2 \times 1 + 3 \times 1 + 4 \times 1}} \cr
& \Rightarrow \frac{{18 + 27 + 36}}{{2 + 3 + 4}} \cr
& \Rightarrow \frac{{81}}{9} \cr
& \Rightarrow 9 \cr} $$
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