If A : B : C = 2 : 3 : 4, then the ratio ^A/_B : ^B/_C : ^C/_A is equal to -

Explanation:-

$$\eqalign{ & {\text{let A}} = 2{\text{k}}, \cr & {\text{B}} = 3{\text{k}} \cr & {\text{C}} = 4{\text{k}}. \cr & {\text{Then,}} \cr & \Rightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{2{\text{k}}}}{{3{\text{k}}}} = \frac{2}{3}, \cr & \Rightarrow \frac{{\text{B}}}{{\text{C}}} = \frac{{3{\text{k}}}}{{4{\text{k}}}} = \frac{3}{4}, \cr & \Rightarrow \frac{{\text{C}}}{{\text{A}}} = \frac{{4{\text{k}}}}{{2{\text{k}}}} = 2. \cr & \Rightarrow \frac{{\text{A}}}{{\text{B}}}:\frac{{\text{B}}}{{\text{C}}}:\frac{{\text{C}}}{{\text{A}}} = \frac{2}{3}:\frac{3}{4}:2 \cr & = 8:9:24. \cr}$$