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

A. 1 : 2 : 6

B. 2 : 3 : 3

C. 3 : 2 : 6

D. 9 : 6 : 4

Solution:

\begin{aligned} = A : B = \frac{1}{2} : \frac{1}{3} = 3 : 2, \\ = B : C = \frac{1}{2} : \frac{1}{3} = 3 : 2 \\ = (3 \times \frac{2}{3}) : (2 \times \frac{2}{3}) \\ = 2 : \frac{4}{3} . \\ \Rightarrow A : B : C = 3 : 2 : \frac{4}{3} \\ = 9 : 6 : 4 \end{aligned}

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