Question : If $a: b: c=\frac{1}{4}: \frac{1}{3}: \frac{1}{2}$, then $\frac{a}{b}: \frac{b}{c}: \frac{c}{a}=$?
Option 1: 12 : 9 : 8
Option 2: 9 : 8 : 24
Option 3: 8 : 9 : 24
Option 4: 9 : 12 : 8
Correct Answer: 9 : 8 : 24
Solution :
According to the question
⇒ $a: b: c=\frac{1}{4}: \frac{1}{3}: \frac{1}{2}$
⇒ $a: b: c=\frac{3}{12}: \frac{4}{12}: \frac{6}{12}=3: 4: 6$
Now,
⇒ $\frac{a}{b}$ = $\frac{3}{4}$, $\frac{b}{c}$ = $\frac{2}{3}$, and $\frac{c}{a}$ = $\frac{2}{1}$
So, $\frac{a}{b}$ : $\frac{b}{c}$ : $\frac{c}{a}$ = $\frac{3}{4}$ : $\frac{2}{3}$ : $\frac{2}{1}$ = 9 : 8 : 24
Hence, the correct answer is 9 : 8 : 24.
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