In a class of 65 students and 4 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 40% of the total number of students. How many sweets are there?

### Concept & Logic This problem requires understanding dynamic distributions. The number of sweets given to each individual is dependent on a fixed variable—the total number of students—rather than a fixed number. $$ \text{Total Sweets} = (\text{Students} \times \text{Sweets per Student}) + (\text{Teachers} \times \text{Sweets per Teacher}) $$ ### Step-by-Step Solution * **Given:** Total number of students = 65 Total number of teachers = 4 Sweets per student = 20% of total students Sweets per teacher = 40% of total students * **Calculation:** Step 1: Calculate the number of sweets each student received. Sweets per student = 20% of 65 $ 0.20 \times 65 = 13 $ sweets per student. Step 2: Calculate the number of sweets each teacher received. Sweets per teacher = 40% of 65 $ 0.40 \times 65 = 26 $ sweets per teacher. Step 3: Calculate the total number of sweets distributed. Total sweets for students = $ 65 \times 13 = 845 $ Total sweets for teachers = $ 4 \times 26 = 104 $ Step 4: Sum them up. Total Sweets = $ 845 + 104 = 949 $ ### Exam Strategy & Shortcut Notice that the percentage for teachers (40%) is exactly double the percentage for students (20%). Since 20% of 65 is 13, you immediately know that 40% is 26 without having to calculate the percentage again. Furthermore, use unit digits to quickly verify addition: The last digit of $ 65 \times 13 $ is 5 (since $ 5 \times 3 = 15 $). The last digit of $ 4 \times 26 $ is 4 (since $ 4 \times 6 = 24 $). $ 5 + 4 = 9 $. The answer must end in 9. The only option ending in 9 is 949. ### Common Pitfall A very common reading error is calculating the percentage against the total number of *people* in the class (students + teachers = 69) instead of strictly the total number of *students* (65) as explicitly stated in the problem text. ### Final Answer **Therefore, the correct answer is 949.**