If A : B : C = 2 : 3 : 4, then the ratio $$\frac{{\text{A}}}{{\text{B}}}$$ : $$\frac{{\text{B}}}{{\text{C}}}$$ : $$\frac{{\text{C}}}{{\text{A}}}$$ is equal to –
a) 4 : 9 : 16
b) 8 : 9 : 24
c) 8 : 9 : 12
d) 8 : 9 : 16
Answer: b
Explanation:
$$\eqalign{
& {\text{let A}} = 2{\text{k}},\,{\text{B}} = 3{\text{k,}}\,{\text{C}} = 4{\text{k}} \cr
& \Rightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{2{\text{k}}}}{{3{\text{k}}}} = \frac{2}{3}, \cr
& \Rightarrow \frac{{\text{B}}}{{\text{C}}} = \frac{{3{\text{k}}}}{{4{\text{k}}}} = \frac{3}{4}, \cr
& \Rightarrow \frac{{\text{C}}}{{\text{A}}} = \frac{{4{\text{k}}}}{{2{\text{k}}}} = 2 \cr
& \frac{{\text{A}}}{{\text{B}}}:\frac{{\text{B}}}{{\text{C}}}:\frac{{\text{C}}}{{\text{A}}} = \frac{2}{3}:\frac{3}{4}:2 \cr
& = 8:9:24 \cr} $$
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