Explanation:

To solve the problem, let's break it down clearly:

- Ratio of boys to girls = 8:5. If there are 8 boys, there are 5 girls.

- Let the number of boys be 8k and girls be 5k, where k is a constant.

- Average age of the whole class = x.

- Average age of girls = x - 2.

Let's find the average age of boys:

1. Total age of the class = Total number * Average age = (8k + 5k) * x = 13kx.

2. Total age of girls = Number of girls * Average age of girls = 5k * (x - 2) = 5kx - 10k.

3. Total age of boys = Total age of class - Total age of girls = 13kx - (5kx - 10k) = 8kx + 10k.

4. Average age of boys = Total age of boys / Number of boys = (8kx + 10k) / 8k = x + 1.25.

Now, check the options:

- Option 1: x - 1.25

- Option 2: x + 1.25

- Option 3: x + 2

- Option 4: x - 2

- Option 5: x + 2.5

Option 2: x + 1.25 is correct.