If $\frac{x}{y}=2$, then $\frac{x-y}{x}$ is equal to:
(a) -1 ;
(b) $-\frac{1}{2}$;
(c) $\frac{1}{2}$;
(d) 1 ;
(e) 2 ;
The correct option is (c).

Solution 1: We have $\frac{x-y}{x}=\frac{x}{x}-\frac{y}{x}=1-\frac{y}{x}$ and, since $\frac{x}{y}=2$, it follows that $\frac{y}{x}=\frac{1}{2}$ and, therefore,

$$
\frac{x-y}{x}=\frac{x}{x}-\frac{y}{x}=1-\frac{1}{2}=\frac{1}{2}
$$

Solution 2: If $\frac{x}{y}=2$, then $x=2 y$ and, therefore, $\frac{x-y}{x}=\frac{2 y-y}{2 y}=\frac{y}{2 y}=\frac{1}{2}$.