In a class of 100 students the average weight is 30 kg. If the average weight of the girls is 24 kg and the average weight of the boys is 32 kg, how many girls are there in the class?

Introduction:
This problem is about using weighted averages to find how many members belong to each subgroup. The overall average weight of the class and the separate average weights of boys and girls are given. We must find the number of girls in the class.

Given Data / Assumptions:
- Total number of students in the class = 100. - Overall average weight of the class = 30 kg. - Average weight of the girls = 24 kg. - Average weight of the boys = 32 kg. - We must find how many girls are in the class.

Concept / Approach:
Let the number of girls be g and the number of boys be 100 - g. The total weight of the girls is 24g and the total weight of the boys is 32(100 - g). The total weight of all 100 students is 30 * 100. Equating the expression from the subgroup weights to the expression from the overall average gives an equation in g which can be solved.

Step-by-Step Solution:
Step 1: Let the number of girls be g. Step 2: Then the number of boys is 100 - g. Step 3: Total weight of all the girls = 24g kg. Step 4: Total weight of all the boys = 32(100 - g) kg. Step 5: Total weight of all 100 students based on overall average = 100 * 30 = 3000 kg. Step 6: Set up the equation: 24g + 32(100 - g) = 3000. Step 7: Expand the right part: 32(100 - g) = 3200 - 32g. Step 8: Substitute back: 24g + 3200 - 32g = 3000. Step 9: Combine like terms: (24g - 32g) + 3200 = 3000 gives -8g + 3200 = 3000. Step 10: Subtract 3200 from both sides: -8g = 3000 - 3200 = -200. Step 11: Divide by -8: g = (-200) / (-8) = 25.

Verification / Alternative Check:
If there are 25 girls, then there are 75 boys. Total weight of girls = 24 * 25 = 600 kg. Total weight of boys = 32 * 75 = 2400 kg. Combined total = 600 + 2400 = 3000 kg. Dividing by 100 students gives an average weight = 3000 / 100 = 30 kg, which matches the given overall average. This verifies that g = 25 is correct.

Why Other Options Are Wrong:
Options 26, 27, 28 and 30 do not satisfy the equation 24g + 32(100 - g) = 3000. For each of these values, the combined total weight would differ from 3000 kg, giving a different overall average than 30 kg.

Common Pitfalls:
A typical error is to attempt to average 24 and 32 directly without accounting for the numbers of boys and girls, or to mis-handle the algebra when combining terms. Keeping separate expressions for total weights and using the overall average formula helps to set up the correct equation.

Final Answer:
The number of girls in the class is 25.