Solution:

The sum of the ages of all the fifth-graders and their parents is: $$33\cdot 11+55\cdot 33 = 66\cdot 33.$$

Then, as the average is the sum divided by the number of people, the average age must be: $$\dfrac{66\cdot 33}{88} = \dfrac 34 \cdot 33 = 24.75 .$$

Thus, the correct answer is C .