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1. If A : B : C = 2 : 3 : 4, then ratio $\frac{A}{B}$ : $\frac{B}{C}$ : $\frac{C}{A}$ is equal to?

A. 8 : 9 : 16

B. 8 : 9 : 12

C. 8 : 9 : 24

D. 4 : 9 : 12

Solution:

\begin{aligned} A : B : C = 2 : 3 : 4 \\ Let \\ A = 2 x, B = 3 x, C = 4 x \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} = \frac{2 x}{3 x} : \frac{3 x}{4 x} : \frac{4 x}{2 x} \\ \Rightarrow \frac{2}{3} : \frac{3}{4} : \frac{2}{1} \end{aligned}

Multiply by the L.C.M of denominator to remove fraction

\begin{aligned} So, \\ L .C .M of (3, 4, 1) = 12 \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \\ \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 \\ 8 : 9 : 24 \end{aligned}

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