The mean of marks secured by 60 students in Division A of Class X is 64, for 40 students in Division B is 60 and for 60 students in Division C is 58. Find the mean of marks of all the students of the three divisions of Class X.

Introduction / Context:
Once again, this problem asks you to find a combined mean for multiple divisions of a class, each with its own average marks and number of students. Handling such questions correctly strengthens your understanding of weighted averages, which are very important in exams and real world data analysis.

Given Data / Assumptions:

• Division A: 60 students with mean marks 64.
• Division B: 40 students with mean marks 60.
• Division C: 60 students with mean marks 58.
• We are to find the overall mean marks of all students from the three divisions combined.

Concept / Approach:
As before, the combined mean is computed using the total marks of all divisions divided by the total number of students. Each division contributes its mean multiplied by its number of students to the grand total. Because the divisions have different means and strengths, this is a classic weighted mean situation.

Step-by-Step Solution:
Step 1: Total marks of Division A = 60 * 64 = 3840. Step 2: Total marks of Division B = 40 * 60 = 2400. Step 3: Total marks of Division C = 60 * 58 = 3480. Step 4: Grand total marks = 3840 + 2400 + 3480 = 9720. Step 5: Total number of students = 60 + 40 + 60 = 160. Step 6: Combined mean marks = 9720 / 160 = 60.75.

Verification / Alternative check:
The group means are 64, 60 and 58. Divisions A and C have the same strength, while Division B is smaller. So the combined mean should be closer to the average of 64 and 58 than to 60 alone. The mean of 64 and 58 is 61, and the presence of Division B with mean 60 pulls the final answer slightly below 61, giving 60.75, which matches our calculation.

Why Other Options Are Wrong:
Option 60.05 and 59.35 are too low and would correspond to total marks much less than 9720. Option 62.15 is too high and would require a larger total than the sums of each division provide. Only 60.75 matches the total marks and respects the positions and sizes of the divisions.

Common Pitfalls:
Problems often arise from calculation errors in the products 60 * 64 or 60 * 58, or from ignoring the weights and simply averaging the three means. Always double check your arithmetic and remember that the final average must fall between the minimum and maximum of the group means.

Final Answer:
The combined mean marks of all students in the three divisions is 60.75.