It's sensible, but pointlessly hard :-)
Expanding the expression of his approach: 60% of the trays contain cups, 84% of the trays contain plates. 100% of the trays (no more, no less!) contain a cup, a plate or both. There are 100% - 60% = 40% of the trays that do NOT contain a cup, so these must be among the 84% of the trays that contain a plate. The remaining 84% - 40% = 44% of the trays that contain a plate must be the ones that contain both. 44% of the 25 trays is 11 trays.
The reason why it's pointlessly hard is that this is strictly easier (generated by copying, pasting and simplifying):
15 of the trays contain cups, 21 of the trays contain plates. 25 of the trays (no more, no less!) contain a cup, a plate or both. There are 25 - 15 = 10 of the trays that do NOT contain a cup, so these must be among the 21 of the trays that contain a plate. The remaining 21 - 10 = 11 of the trays that contain a plate must be the ones that contain both.
If I were you, I'd make sure he understands exactly why his method was correct, but unnecessarily hard (e.g., show him this post), just to make sure he wouldn't get stuck on a problem that didn't allow for being turned easily into percentages!
