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: Option C

Solution(By Examveda Team)

$$\eqalign{ & x = \frac{1}{3}y\,\,{\text{and }}y = \frac{1}{2}z \cr & \frac{x}{y} = \frac{1}{3}\,{\text{and }}\frac{y}{z} = \frac{1}{2} \cr & x:y = 1:3 \cr & y:z = 1:2 \times 3\,({\text{multiply}}) \cr & i.e.\,y:z = 3:6 \cr & \therefore x:y:z = 1:3:6 \cr} $$