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

Answer: Option C

$$\begin{array}{rl}& \text{A}:\text{B}:\text{C}=2:3:4\\ & \text{Let }\\ & \text{A}=2x,\text{B}=3x,\text{C}=4x\\ & \therefore \frac{\text{A}}{\text{B}}:\frac{\text{B}}{\text{C}}:\frac{\text{C}}{\text{A}}=\frac{2x}{3x}:\frac{3x}{4x}:\frac{4x}{2x}\\ & \Rightarrow \frac{2}{3}:\frac{3}{4}:\frac{2}{1}\end{array}$$
Multiply by the L.C.M of denominator to remove fraction
$$\begin{array}{rl}& \text{So,}\\ & \text{L}\text{.C}\text{.M of }\left(3,4,1\right)=12\\ & \therefore \frac{\text{A}}{\text{B}}:\frac{\text{B}}{\text{C}}:\frac{\text{C}}{\text{A}}\\ & \frac{2}{3}\times 12:\frac{3}{4}\times 12:\frac{2}{1}\times 12\\ & 8:9:24\end{array}$$