The two science classes 7A and 7B each consist of a number of boys and a number of girls. Each class has exactly 30 students.The girls in 7A have a mean score of 48. The overall mean across both classes is 60.The mean score across all the girls of both classes is also 60.The 5 girls in 7B have a mean score that is double that of the 15 boys in 7A.The mean score of the boys in 7B is 𝜇. What is the value of 10𝜇?

To solve this problem, we need to break it down into several steps:

1. First, we know that each class has 30 students, so there are 60 students in total. The overall mean score across both classes is 60, so the total score for all students is 60 * 60 = 3600.

2. We know that the girls in 7A have a mean score of 48. If we let G be the number of girls in 7A, then the total score for the girls in 7A is 48 * G.

3. We also know that the mean score across all the girls in both classes is 60. If we let H be the total number of girls in both classes, then the total score for all the girls is 60 * H.

4. We know that the 5 girls in 7B have a mean score that is double that of the 15 boys in 7A. So, the total score for the girls in 7B is 2 * 15 * B, where B is the mean score of the boys in 7A.

5. We also know that the mean score of the boys in 7B is 𝜇. If we let J be the number of boys in 7B, then the total score for the boys in 7B is 𝜇 * J.

6. We can now set up the following equation based on the information above: 48 * G + 60 * H + 2 * 15 * B + 𝜇 * J = 3600.

7. We also know that G + H + 15 + J = 60, because there are 60 students in total.

8. We can solve these two equations to find the values of G, H, B, J, and 𝜇. Once we have the value of 𝜇, we can find the value of 10𝜇.

Without the specific numbers of boys and girls in each class, we cannot solve this problem completely. However, this is the general approach you would take to solve it.