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Answer :
To solve this problem, we need to find the average weight of the 10 girls in the class. Let's break it down step-by-step.
First, let's understand what we know:
- The average weight of all 30 students (20 boys and 10 girls) is 50 kg.
- If we exclude the weights of the 10 girls, the average weight of the remaining 20 boys decreases by 5 kg, meaning their new average weight is 45 kg.
Using this information, we can calculate the total weight of each group (entire class, just the boys, and just the girls).
Step 1: Calculate the total weight of all students.
[tex]\text{Total weight of 30 students} = 30 \times 50 = 1500 \text{ kg}[/tex]
Step 2: Calculate the total weight of the 20 boys.
When the girls are excluded, the average weight of the remaining 20 boys is 45 kg. Therefore:
[tex]\text{Total weight of 20 boys} = 20 \times 45 = 900 \text{ kg}[/tex]
Step 3: Calculate the total weight of the 10 girls.
The total weight of the 10 girls can be found by subtracting the total weight of the boys from the total weight of all students:
[tex]\text{Total weight of 10 girls} = 1500 - 900 = 600 \text{ kg}[/tex]
Step 4: Calculate the average weight of the 10 girls.
The average weight of these 10 girls is:
[tex]\text{Average weight of 10 girls} = \frac{600}{10} = 60 \text{ kg}[/tex]
Therefore, the average weight of all 10 girls is [tex]\boxed{60 \text{ kg}}[/tex]. This corresponds to option A.
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