In a class of 60 students there are 20 girls who scored an average of 40 marks in a test. If the average marks of the whole class is 60, what are the average marks of the boys in the class?

Introduction / Context:
This question deals with averages of two subgroups (boys and girls) inside a larger group (the whole class). You are given the class average and the girls' average and asked to find the boys' average. This is a very typical weighted average problem seen in basic quantitative aptitude tests.

Given Data / Assumptions:

Total students in the class = 60.
Number of girls = 20, so number of boys = 60 - 20 = 40.
Average marks of the girls = 40 marks.
Average marks of the entire class = 60 marks.
Marks are all from the same test and on the same scale.

Concept / Approach:
Average marks multiplied by the number of students gives total marks. So we first compute the total marks of the entire class using the overall average, and the total marks of the girls using their average. Subtracting the girls' total from the class total yields the total marks scored by the boys. Dividing that total by the number of boys produces the boys' average marks.

Step-by-Step Solution:
Step 1: Total marks scored by all 60 students. Total class marks = 60 * 60 = 3600. Step 2: Total marks scored by 20 girls. Girls' total marks = 20 * 40 = 800. Step 3: Total marks scored by 40 boys. Boys' total marks = 3600 - 800 = 2800. Step 4: Average marks of the boys. Average boys' marks = 2800 / 40 = 70.

Verification / Alternative Check:
We can quickly verify by recombining the subgroup totals. Girls contribute 800 marks and boys contribute 2800 marks. Combined total = 3600 marks. Dividing by the total of 60 students, we get 3600 / 60 = 60 marks, which matches the original overall average. This confirms that the boys' average of 70 marks is consistent with the entire scenario.

Why Other Options Are Wrong:
60 would imply that boys and class have the same average, which is impossible because girls score lower on average (40), so boys must score higher to pull the class average up to 60.
50 would pull the overall class average down below 60 when combined with girls averaging 40.
80 would make the class average higher than 60 because boys are a majority (40 out of 60) and such a high average would dominate the combined score.

Common Pitfalls:
A common error is to directly average 40 and 60, ignoring that there are more boys than girls. Some learners also forget to compute totals and rely on intuition about how averages combine. Always translate average information into totals first when dealing with subgroups, then work backwards to find the missing average.

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