If $$x = \frac{1}{3}y$$ and $$y = \frac{1}{2}z{\text{,}}$$ then x : y : z is equal to = ?
a) 3 : 2 : 1
b) 1 : 2 : 6
c) 1 : 3 : 6
d) 2 : 4 : 6
Answer: c
Explanation:
$$\eqalign{
& x = \frac{1}{3}y\,\,{\text{and }}y = \frac{1}{2}z \cr
& \frac{x}{y} = \frac{1}{3}\,{\text{and }}\frac{y}{z} = \frac{1}{2} \cr
& x:y = 1:3 \cr
& y:z = 1:2 \times 3\,({\text{multiply}}) \cr
& i.e.\,y:z = 3:6 \cr
& x:y:z = 1:3:6 \cr} $$
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