A class consists of 30 students. Each of them has registered for 5 courses. Each course instructor conducts an exam of 200 marks. The average percentage marks of all 30 students across all courses they have registered for is 80%. Two of them apply for revaluation in a course. If none of their marks reduce, and the average of all 30 students across all courses becomes 80.02%, the maximum possible increase in marks for either of the 2 students is

There are 30 students, and each of them has registered for five courses. Each course instructor administers a 200-mark exam. Thus, the total maximum marks for all the students around all the courses $$=30\times5\times200=30000$$

The average percentage marks of all 30 students across all courses they have registered for is 80%. This means their total score is $$0.8\times3000=24000$$

Now, two of them gave their copies for reevaluation, and none of their mark decreased. After this, the percentage increased to 80.02%. Thus, after reevaluation, the total score will be $$\dfrac{80.02}{100}\times30000=24006$$.

We can see that there is an increase of 6 marks. Thus, the maximum possible increase in marks for either of the 2 students will be 6 marks.