In a class the ratio of the number of boys to the number of girls is 2 : 3. The average weight of the boys is 18 kg and the average weight of the girls is 21 kg. What is the average weight, in kg, of all the students together?

Introduction / Context:
This question tests understanding of weighted averages when group sizes differ. The class has boys and girls in a fixed ratio, and their separate average weights are given. We must find the combined average weight of all students.

Given Data / Assumptions:
- Ratio of boys : girls = 2 : 3. - Average weight of boys = 18 kg. - Average weight of girls = 21 kg. - We assume all students are counted once and weights are in kilograms.

Concept / Approach:
Choose convenient absolute numbers consistent with the ratio, for example 2 boys and 3 girls. Their total weight can be computed using the given averages. The overall average weight is then total weight divided by total number of students. Because averages depend only on relative ratios, the result will be the same for any scaled group sizes with ratio 2 : 3.

Step-by-Step Solution:
Step 1: Assume there are 2 boys and 3 girls. Step 2: Total weight of boys = 2 * 18 = 36 kg. Step 3: Total weight of girls = 3 * 21 = 63 kg. Step 4: Total weight of all students = 36 + 63 = 99 kg. Step 5: Total number of students = 2 + 3 = 5. Step 6: Average weight = total weight / total students = 99 / 5 kg. Step 7: 99 / 5 = 19.8 kg if expressed as a decimal.

Verification / Alternative check:
Alternatively, use the weighted average formula directly. Overall average = (2 * 18 + 3 * 21) / (2 + 3). This equals (36 + 63) / 5 = 99 / 5, perfectly matching the earlier calculation. This confirms that the chosen counts respect the ratio and yield the correct combined average.

Why Other Options Are Wrong:
- 101/5, 96/5 and 109/6 represent different overall totals or weights and do not match the correct weighted sum. - 21 kg would be the average only if all students had the same average as the girls, ignoring the lighter boys.

Common Pitfalls:
Many learners simply average 18 and 21 without weighting, which ignores the fact that there are more girls than boys. Others misuse the ratio and pick wrong counts. Always multiply each group average by its relative group size to form the correct weighted sum before dividing by the total count.

Final Answer:
The average weight of all students together is 99/5 kg.