Explanation:

- The average of 12 numbers is 25.5. This means their sum is \(12 \times 25.5 = 306\).

- The average of the first six numbers is 22.4, so their sum is \(6 \times 22.4 = 134.4\).

- The average of the last three numbers is 28.2, meaning their sum is \(3 \times 28.2 = 84.6\).

- Therefore, the sum of the 7th, 8th, and 9th numbers is \(306 - 134.4 - 84.6 = 87\).

- Given: \(7^{th} = 8^{th} - 5\) and \(7^{th} = 9^{th} - 10\).

- Let 8th number be x; then 7th = \(x - 5\), and 9th = \(x + 5\).

- Then, \((x - 5) + x + (x + 5) = 87\), simplifying to \(3x = 87\), so \(x = 29\).

- 9th number is \(x + 5 = 34\).

- Average of 8th and 9th numbers = \((29 + 34)/2 = 31.5\).

- Correct Answer: Option 4, 31.5

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