Explanation:

Let's solve the problem to find x : y.

- Given: \( (6x + 5y) : (6x - 5y) = 11 : 5 \)

- Write as equation: \( \frac{6x + 5y}{6x - 5y} = \frac{11}{5} \)

- Cross-multiply: \( 5(6x + 5y) = 11(6x - 5y) \)

- Expand: \( 30x + 25y = 66x - 55y \)

- Rearrange: \( 25y + 55y = 66x - 30x \)

- Simplify: \( 80y = 36x \)

- Solve for ratio: \( x : y = 80 : 36 = 20 : 9 \)

- Option 1: 20 : 9

- Option 2: 12 : 5

- Option 3: 15 : 8

- Option 4: 18 : 11

The correct answer is 20 : 9.

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