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
Solution 1: We have:

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

Since $\frac{x}{y}=2$ we have $\frac{y}{x}=\frac{1}{2}$, thus

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

The correct option is (c).

Solution 2: If $\frac{x}{y}=2$, then $x=2 y$. Therefore

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