When we add the number of cups (15) to the number of plates (21) we can look at it as counting all trays with cups only, all trays with plates only, and double the number of trays with both cups and plates (we count those trays from both the cups and the plates side). Since there are no empty trays, cups only + plates only + cups/plates counted once gives us the total number of trays, which is 25. What is left (the difference between 15+21 and 25) is that extra counted number of cups/plates trays. So the solution is (15+21)-25=11.
The solution with percentages uses the same approach but adds an extra level of complexity to calculations. It transforms numbers to percentages at the beginning, and at the end converts percentages back to numbers: (60%+84%)-100%=44%.
