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.

If (x - 2y) : (2x - y) = 1 : 3, find x : y

Learn how to solve the ratio problem where (x - 2y) : (2x - y) = 1 : 3 using algebraic cross-multiplication. This solution explores key concepts in ratios and algebra, perfect for students in Grades 8-10.

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