In a class there are 28 boys and some girls. The average score of the boys in a test is 12.5, while the average score of the girls is 14.5. If the overall average score of all students is 13.1, how many students are there in the class in total?

Introduction / Context:
This problem involves combining averages from two subgroups (boys and girls) to obtain the overall class average and then working backwards to deduce the unknown group size. It is a practical example of weighted averages, where each group contributes according to its size and mean score. Such questions are standard in quantitative aptitude tests.

Given Data / Assumptions:

• Number of boys = 28.
• Average score of boys = 12.5.
• Average score of girls = 14.5.
• Overall average score of the class = 13.1.
• Number of girls is unknown; let it be g.

Concept / Approach:
The key is to convert each average into a total score and then set up an equation. The total score of boys is fixed, the total score of girls depends on g, and their sum must equal the overall average multiplied by the total number of students (28 + g). Solving this equation gives g, and so we can find the total students.

Step-by-Step Solution:
Step 1: Total score of boys = 28 * 12.5 = 350.Step 2: Total score of girls = 14.5 * g.Step 3: Total number of students = 28 + g, so overall total score = 13.1 * (28 + g).Step 4: Set up equation: 350 + 14.5g = 13.1(28 + g).Step 5: Compute right side: 13.1 * 28 = 366.8, so 350 + 14.5g = 366.8 + 13.1g.Step 6: Simplify: 14.5g - 13.1g = 366.8 - 350, so 1.4g = 16.8, hence g = 12.Step 7: Total students = 28 + 12 = 40.

Verification / Alternative check:
Check totals: Boys total = 350, girls total = 12 * 14.5 = 174, combined total = 524. Average = 524 / 40 = 13.1, which matches the given overall average, confirming that 40 is correct.

Why Other Options Are Wrong:
Options 42, 44, or 38 would correspond to different values of g and would break the relationship between subgroup averages and the overall average. Substituting those totals back into the equation would not produce an overall average of 13.1. Option 36 similarly fails to satisfy the weighted average condition.

Common Pitfalls:

• Using a simple unweighted average of 12.5 and 14.5 instead of considering the number of boys and girls.
• Arithmetic mistakes when distributing 13.1 or simplifying the equation.
• Forgetting that total students are 28 + g, not just g.

Final Answer:
The total number of students in the class is 40.