The average weight of 24 boys and 6 girls in a class is 40 kg. If the weight of all the girls excluded the average weight of the class is reduced by 4 kg, then find the average weight of all the six girls?

Correct Answer: Option B (56 kg)

Step-by-step Explanation:

Step 1: Understand the given data

Number of boys in the class = 24

Number of girls in the class = 6

Total number of students in the class = 24 + 6 = 30 students

Initial average weight of the entire class (30 students) = 40 kg

Step 2: Calculate the total weight of the class

The total weight of all 30 students can be calculated using the average formula:

$\text{Total Weight}=\text{Average Weight}\times \text{Total Students}$

Substituting the values:

$\text{Total Weight of 30 students}=40\times 30=1200\text{kg}$

Step 3: Calculate the new total weight after excluding the girls

When the weight of all 6 girls is excluded, only the 24 boys remain in the class.

The average weight of the remaining students (24 boys) is reduced by 4 kg.

New average weight of 24 boys = 40 - 4 = 36 kg

Now, calculate the total weight of the 24 boys:

$\text{Total Weight of 24 boys}=36\times 24=864\text{kg}$

Step 4: Calculate the total weight of the 6 girls

The total weight of the 6 girls is the difference between the total weight of the entire class and the total weight of the 24 boys:

$\text{Total Weight of 6 girls}=1200-864=336\text{kg}$

Step 5: Find the average weight of the 6 girls

Now, divide the total weight of the 6 girls by the number of girls:

$\text{Average Weight of 6 girls}=\frac{336}{6}=56\text{kg}$

Thus, the average weight of all six girls is 56 kg.