Explanation:

- The average age of the three girls is given as 24 years.

- Therefore, the sum of their ages is 3 multiplied by 24, which equals 72 years.

- Their ages are in the ratio 7:8:9. Let's represent their ages as 7x, 8x, and 9x.

- Adding the ages together, we have 7x + 8x + 9x = 72.

- Simplifying, we get 24x = 72.

- Solving for x, we find x = 3.

- We can calculate the ages: 7x = 21, 8x = 24, and 9x = 27.

- The eldest girl is thus 27 years old.

Correct Answer: Option 4 - 27 years