The given ratio is:

$\frac{x - 2y}{2x - y} = \frac{1}{3}$

To solve for $x : y$, we can cross-multiply the terms:

$3(x - 2y) = 1(2x - y)$

Expanding both sides:

$3x - 6y = 2x - y$

Now, simplify the equation by subtracting $2x$ from both sides:

$x - 6y = -y$

Next, add $6y$ to both sides:

$x = 5y$

This means the ratio of $x : y = 5 : 1$.

Would you like a detailed explanation on any part of the solution?

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Here are 5 related questions for further exploration:

1. How do you cross-multiply when dealing with ratios?
2. How do you convert a ratio equation to a linear equation?
3. What are some methods to check if a ratio is correctly simplified?
4. How can ratios be applied in geometry?
5. What happens when you have a ratio with variables in both parts?

Tip: When solving ratio problems, cross-multiplying is a powerful technique to eliminate fractions.