If A : B : C = 2 : 3 : 4, then A B : B C : C A is equal to?

Answer: Option C

$$\begin{array}{rl}& \text{A}:\text{B}:\text{C}\\ & 2:3:4\\ & \therefore \frac{\text{A}}{\text{B}}:\frac{\text{B}}{\text{C}}:\frac{\text{C}}{\text{A}}\\ & \left(\text{multiply with ABC}\right)\\ & \therefore \frac{\text{A}\times \text{ABC}}{\text{B}}\text{:}\frac{\text{B}\times \text{ABC}}{\text{C}}\text{:}\frac{\text{C}\times \text{ABC}}{\text{A}}\\ & \Rightarrow {\text{A}}^2\text{C}:{\text{B}}^2\text{A}:\text{B}{\text{C}}^2\\ & \Rightarrow {\left(2\right)}^2\times 4:{\left(3\right)}^2\times 2:{\left(4\right)}^2\times 3\\ & \Rightarrow 16:18:48\\ & \Rightarrow 8:9:24\\ & \\ & \mathbf{Alternate}:\\ & \frac{\text{A}}{\text{B}}:\frac{\text{B}}{\text{C}}:\frac{\text{C}}{\text{A}}=\frac{2}{3}:\frac{3}{4}:\frac{4}{2}\\ & \Rightarrow \frac{2}{3}\times 12:\frac{3}{4}\times 12:\frac{4}{2}\times 12\\ & \Rightarrow 8:9:24\end{array}$$