If the average of 10 numbers is 3.1, the sum of the numbers is 31. If the average of the remaining 5 numbers is 2.85, the sum of those remaining 5 numbers is 5(2.85) = 14.25. The sum of the discarded numbers, then, is 31 - 14.25 = 16.75.
The average of the discarded numbers is 16.75/5 = 3.35, choice (C).
Note that because the original group of 10 numbers is split into two groups of 5, we could've avoided some of the work. If the average of the entire group is 3.1 and the average of half of the group is 0.25 less than that (2.85), the average of the other half must be 0.25 more, 3.35.