Question : If $A:B: C=2:3:4$, then what will be the value of $\frac{A}{B}:\frac{B}{C}:\frac{C}{A}$?
Option 1: $9: 5: 36$
Option 2: $8: 7: 25$
Option 3: $8: 9: 24$
Option 4: $12: 10: 13$
Correct Answer: $8: 9: 24$
Solution :
Let's denote $k$ as a constant. Given that $A :B : C = 2 :3 :4$
⇒ $A = 2k,B = 3k,$ and $C = 4k$
So, $\frac{A}{B} = \frac{2k}{3k}=\frac{2}{3}$
⇒ $\frac{C}{D} = \frac{3k}{4k}=\frac{3}{4}$
⇒ $\frac{C}{A} = \frac{4k}{2k} = \frac{2}{1}$
So, the values of $\frac{A}{B}$ : $\frac{C}{D}$ : $\frac{C}{A}=\frac{2}{3}$ : $\frac{3}{4}$ : ${2} = 8 : 9: 24$
Hence, the correct answer is $8 : 9: 24$.
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