In a class there are 28 boys and some girls. In a test, the mean score obtained by the boys is 12.5, while the mean score obtained by the girls is 14.5. If the overall average score of all the students is 13.1, what is the total number of students in the class?

Introduction / Context:
This problem is another weighted average question where you know the averages of two subgroups (boys and girls) and the combined average of the class. The number of boys is known, but the number of girls is unknown. You must use the relationship between group totals and the overall average to find the total class size.

Given Data / Assumptions:

Number of boys = 28.
Mean score of boys = 12.5 marks.
Mean score of girls = 14.5 marks.
Overall mean score of all students = 13.1 marks.
Let the number of girls be g, and total students be 28 + g.

Concept / Approach:
The total marks of boys plus the total marks of girls must equal the overall mean multiplied by the total number of students. We compute the total marks of the boys using their mean and number. Then we represent the total marks of the girls using g and their mean. Setting the sum equal to 13.1 * (28 + g) gives an equation in g, which we solve. Once we find g, we add it to 28 to get the total class strength.

Step-by-Step Solution:
Step 1: Compute total marks of the boys. Total boys' marks = 28 * 12.5 = 350. Step 2: Express total marks of the girls in terms of g. Mean score of girls = 14.5, so total girls' marks = 14.5 * g. Step 3: Use the overall mean condition. Overall mean = 13.1 marks. Total class marks = 13.1 * (28 + g). Equation: 350 + 14.5g = 13.1 * (28 + g). Step 4: Solve for g. 13.1 * (28 + g) = 13.1 * 28 + 13.1g = 366.8 + 13.1g. So 350 + 14.5g = 366.8 + 13.1g. 14.5g - 13.1g = 366.8 - 350 → 1.4g = 16.8. g = 16.8 / 1.4 = 12. Step 5: Find total number of students. Total students = 28 + 12 = 40.

Verification / Alternative Check:
With 12 girls, total girls' marks = 14.5 * 12 = 174. Total marks for the class = 350 + 174 = 524. Dividing this by 40 students gives 524 / 40 = 13.1, which matches the given overall average, confirming that the class has 40 students.

Why Other Options Are Wrong:
38 or 42 or 44 would correspond to different values of g, and substituting those values back into the equation would not produce an overall average of 13.1. Only g = 12 gives a consistent solution.

Common Pitfalls:
Some learners incorrectly attempt to average 12.5 and 14.5 directly, ignoring the different numbers of boys and girls. Others make algebraic errors when expanding and simplifying the equation, especially with decimals. Carefully computing the totals for each subgroup and then solving the linear equation step by step helps avoid these mistakes.

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