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

Introduction / Context:
This question uses the concept of weighted averages to relate the average weight of a subgroup (girls), the overall class average, and the unknown average weight of the complementary subgroup (boys). Such questions are very common in aptitude tests and help to strengthen understanding of averages in mixed groups.

Given Data / Assumptions:

• Total number of students in the class = 60.
• Number of girls = 30.
• Number of boys = 60 - 30 = 30.
• Average weight of girls = 58 kg.
• Average weight of the entire class = 63 kg.
• We assume all weights are measured accurately in kilograms.

Concept / Approach:
The central idea is that: Total weight of all students = average weight of class * number of students. Similarly, the total weight of girls is average of girls times their count, and the total weight of boys is average of boys times their count. The total class weight is also equal to the sum of the weights of girls and boys. Using these relations we can solve for the unknown average weight of the boys.

Step-by-Step Solution:
Step 1: Compute total weight of all 60 students. Total class weight = 63 * 60 = 3780 kg. Step 2: Compute total weight of the 30 girls. Total weight of girls = 58 * 30 = 1740 kg. Step 3: Compute total weight of the boys. Total weight of boys = total class weight - total girls weight. Total weight of boys = 3780 - 1740 = 2040 kg. Step 4: Compute average weight of the boys. Average weight of boys = 2040 / 30 = 68 kg.

Verification / Alternative check:
We can verify by recomputing the combined average using boys average 68 and girls average 58. Combined average = (30 * 58 + 30 * 68) / (30 + 30) = (1740 + 2040) / 60 = 3780 / 60 = 63 kg, which matches the given overall average, confirming the result is consistent.

Why Other Options Are Wrong:
If the boys average were 67, the total boys weight would be 30 * 67 = 2010 kg, giving class total 2010 + 1740 = 3750 kg and class average 3750 / 60 = 62.5 kg, not 63 kg. For 66 kg, the class average becomes even lower. For 65 kg, it reduces further. Only an average of 68 kg for the boys restores the overall average to 63 kg as given in the question.

Common Pitfalls:
A common mistake is to take the simple average of 58 and 63, which ignores the fact that both groups have equal strength here but may not in other questions. Another pitfall is confusing total and average, or attempting to directly manipulate averages without first converting them into totals. Always convert averages to totals using total = average * number of items, then combine and reconvert back into averages.

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