Explanation:

- We know the average of 10 consecutive even numbers is 25.

- The sum of these numbers is \( 25 \times 10 = 250 \).

- Denote the smallest even number as \( 2n \).

- Then the numbers are \( 2n, 2n+2, ..., 2n+18 \).

- The sum of these numbers: \( 10 \times 2n + 90 = 250 \), solving gives \( 2n = 16 \).

- So, the numbers are 16, 18, 20, ..., 34.

- Include the preceding number: 14.

- The sum of these 11 numbers is \( 250 + 14 = 264 \).

- The new average is \( \frac{264}{11} = 24 \).

- Option 4 (24) is the correct answer.