The average weight of 20 boys and 10 girls in a class is 50 kg. If the weight of all the girls is excluded, the average weight of the remaining students decreases by 5 kg. Find the average weight of all 10 girls.

The correct answer is 60 kg.

Let us solve the problem step-by-step:

Step 1: Calculate the total weight of all students (boys and girls).
The number of boys is 20 and the number of girls is 10.
Total number of students in the class = 20 + 10 = 30 students.
The average weight of all 30 students is 50 kg.
Therefore, the total weight of all 30 students is:
$\text{Total Weight}=30\times 50=1500\text{kg}$

Step 2: Calculate the total weight of the boys (remaining students).
If the weight of all the girls is excluded, only the 20 boys remain.
The average weight of the remaining students decreases by 5 kg, which means:
New average weight = 50 kg - 5 kg = 45 kg.
Therefore, the total weight of the 20 boys is:
$\text{Total Weight of Boys}=20\times 45=900\text{kg}$

Step 3: Calculate the total weight of the 10 girls.
The total weight of the girls is the difference between the total weight of all students and the total weight of the boys:
$\text{Total Weight of Girls}=1500-900=600\text{kg}$

Step 4: Find the average weight of the 10 girls.
The average weight is the total weight of the girls divided by the number of girls:
$\text{Average Weight of Girls}=\frac{600}{10}=60\text{kg}$