Solution:

Given:
- Total number of students = 40
- Average weight of existing students = 40 kgs
- Average weight of new students = n kgs
- m*n = 50

To find: Maximum possible average weight of the class

Approach:
- We know that the average weight of the class will increase as the weight of new students added to the class increases.
- To maximize the average weight of the class, we need to add new students with the maximum possible weight.

Calculation:
- Let's assume the number of new students added to the class is 'x'.
- Total number of students in the class after new students join = 40 + x
- Total weight of existing students = 40 * 40 = 1600 kgs
- Total weight of new students = x * n kgs
- Total weight of all students in the class = 1600 + x * n kgs
- Average weight of the class = (1600 + x * n) / (40 + x)

Now, we need to find the value of 'x' and 'n' that will maximize the average weight of the class.

- Given, m * n = 50
- We want to maximize the average weight of the class, which means we want to maximize the numerator (1600 + x * n).
- To maximize the numerator, we need to maximize both 'x' and 'n'.
- But we have a constraint that m * n = 50. So, we need to find the maximum value of 'n' for a given value of 'm' (where m = 40).

- Let's rewrite the equation m * n = 50 as n = 50/m.
- Substituting this value of 'n' in the equation for average weight of the class, we get:
Average weight of the class = (1600 + 50x/m) / (40 + x)

- To maximize the average weight of the class, we need to maximize the numerator (1600 + 50x/m).
- Let's differentiate the numerator w.r.t. 'x' and equate it to zero to find the maximum value of 'x'.
d/dx (1600 + 50x/m) = 50/m = 0
=> x = 40

- Substituting this value of 'x' in the equation for average weight of the class, we get:
Average weight of the class = (1600 + 50*40/m) / (40 + 40) = (1600 + 50) / 80 = 20.63 kgs (approx)

- Therefore, the maximum possible average weight of the class is approximately 20.63 kgs.

Conclusion:
- To maximize the average weight of the class, we need to add new students with the maximum possible weight.
- Based on the given constraint m*n=50, we found the maximum value of 'n' for a given value of 'm'.
- Using this value of 'n', we found the maximum value of 'x' that will maximize the average weight of the class.
- Finally, we calculated the maximum possible average weight of the class, which is approximately 20.63 kgs.