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1. If $x = \frac{1}{3} y$ and $y = \frac{1}{2} z,$ then x : y : z is equal to = ?

A. 3 : 2 : 1

B. 1 : 2 : 6

C. 1 : 3 : 6

D. 2 : 4 : 6

Solution:

\begin{aligned} x = \frac{1}{3} y and y = \frac{1}{2} z \\ \frac{x}{y} = \frac{1}{3} and \frac{y}{z} = \frac{1}{2} \\ x : y = 1 : 3 \\ y : z = 1 : 2 \times 3 (multiply) \\ i . e . y : z = 3 : 6 \\ ∴ x : y : z = 1 : 3 : 6 \end{aligned}

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