In a class of 60 students there are 30 girls. The average weight of these 30 girls is 58 kg and the average weight of the full class is 63 kg. What is the average weight of the boys in the class, in kilograms?

Introduction / Context:
This averages question involves two subgroups within a class, girls and boys. You are told the size and average weight of the girls group, as well as the overall average weight of the entire class. From this information, you must determine the average weight of the boys. This is a classic weighted average problem that appears frequently in aptitude tests.

Given Data / Assumptions:
- Total number of students in the class = 60.
- Number of girls = 30.
- Therefore, number of boys = 60 - 30 = 30.
- Average weight of the girls = 58 kg.
- Average weight of the full class = 63 kg.
- We must find the average weight of the boys in kilograms.

Concept / Approach:
The combined total weight of all students can be computed using the overall average. The total weight of the girls group can be calculated from their average and count. The difference between the combined total and the girls total gives the total weight of the boys. Dividing this by the number of boys yields the average weight of the boys. This approach is an example of decomposing a weighted average into component groups.

Step-by-Step Solution:
Step 1: Compute total weight of all 60 students using the overall average.Step 2: Total weight of class = 60 * 63 = 3780 kg.Step 3: Compute total weight of the 30 girls using their average.Step 4: Total weight of girls = 30 * 58 = 1740 kg.Step 5: Total weight of boys = total class weight - total girls weight = 3780 - 1740 = 2040 kg.Step 6: Number of boys = 30.Step 7: Average weight of boys = total weight of boys / number of boys = 2040 / 30.Step 8: Compute 2040 / 30 = 68 kg.Step 9: Therefore, the average weight of the boys is 68 kg.

Verification / Alternative check:
We can confirm the result by recomputing the combined average. If boys average 68 kg and girls average 58 kg, with 30 of each, then total boys weight is 30 * 68 = 2040 kg and total girls weight is 30 * 58 = 1740 kg. Combined total is 2040 + 1740 = 3780 kg. Dividing 3780 by 60 students gives an overall average of 63 kg, which matches the given data. This confirms that the boys average weight must be 68 kg.

Why Other Options Are Wrong:
If the boys average were 67, 66 or 65 kg, the total combined weight would differ and the overall average would not remain 63 kg. For example, with an average of 66 kg for boys, total boys weight would be 1980 kg, and the class total would be 1980 + 1740 = 3720 kg, which gives an overall average of 3720 / 60 = 62 kg, not 63 kg. Hence these alternatives do not satisfy the conditions.

Common Pitfalls:
Some students attempt to average the two given averages 58 and 63 directly without considering that the group sizes are equal or different. Other students miscalculate the total weights due to simple multiplication errors. Always convert each group average into a group total, sum or subtract as required, and then divide by the correct group size to obtain the missing average.

Final Answer:
The average weight of the boys in the class is 68 kg.