In a class of 65 students, there are 39 girls whose average weight is 60 kg. The average weight of the whole class is 64 kg. What is the average weight of the boys in the class?

Introduction / Context:
This question tests weighted average concepts where there are two groups within a larger group, each with its own average. You are given the overall average as well as the average of one subgroup and asked to compute the average of the remaining subgroup. This is a classic mixture and alligation style situation, useful in aptitude tests and real life when combining data from different segments.

Given Data / Assumptions:

• Total students in the class = 65.
• Number of girls = 39.
• Average weight of girls = 60 kg.
• Average weight of entire class = 64 kg.
• Number of boys = 65 - 39 = 26.

Concept / Approach:
The approach is to translate the average information into totals. The total weight of all students is overall average multiplied by total students. The total weight of the girls is girls average multiplied by number of girls. Subtracting the girls total from the class total gives the total weight of boys. Dividing this by the number of boys yields the average weight of the boys.

Step-by-Step Solution:
Step 1: Total class weight = 64 * 65 = 4160 kg.Step 2: Total weight of girls = 60 * 39 = 2340 kg.Step 3: Total weight of boys = 4160 - 2340 = 1820 kg.Step 4: Number of boys = 26.Step 5: Average weight of boys = 1820 / 26 = 70 kg.

Verification / Alternative check:
We can verify by reconstructing the overall average. Suppose each boy weighs on average 70 kg, so total weight of boys is 26 * 70 = 1820 kg. Adding the girls total of 2340 kg gives 4160 kg. Dividing 4160 by 65 again yields 64 kg, confirming consistency with the given overall average.

Why Other Options Are Wrong:
Option 69 or 68 would reduce the boys total and hence reduce the overall average below 64 kg. Option 66 is even smaller and clearly cannot produce an overall average greater than the given girls average of 60 kg with the given proportions. Option 64 would mean boys and girls have similar weights, which contradicts the requirement of an overall average of 64 with the girls fixed at 60 kg.

Common Pitfalls:

• Using a simple average of 60 and 64 instead of a weighted average based on actual counts.
• Incorrectly computing the number of boys or making arithmetic errors in multiplication.
• Trying to guess the answer without checking against the overall average condition.

Final Answer:
The average weight of the boys in the class is 70 kg.