The average weight of 20 students of a class is 33 kg. If the average weight of all the boys is 35 kg and the average weight of all the eight girls is y kg, then find y

Options

A. 28
B. 39
C. 30
D. 31

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total weight of all students
The average weight of 20 students is given as 33 kg. We can find the total weight (A) of all students using the formula for average:

\[ \text{Total Weight (A)} = \text{Average Weight} \times \text{Number of Students} \]

Substituting the values:

\[ A = 33 \, \text{kg} \times 20 = 660 \, \text{kg} \]

### Step 2: Calculate the total weight of the boys
We know that the average weight of all the boys is 35 kg and there are 12 boys (since there are 20 students in total and 8 are girls). We can find the total weight of the boys using the same formula:

\[ \text{Total Weight of Boys} = \text{Average Weight of Boys} \times \text{Number of Boys} \]

Substituting the values:

\[ \text{Total Weight of Boys} = 35 \, \text{kg} \times 12 = 420 \, \text{kg} \]

### Step 3: Calculate the total weight of the girls
Let the average weight of the girls be \( y \) kg. Since there are 8 girls, the total weight of the girls (C) can be expressed as:

\[ \text{Total Weight of Girls} = y \times 8 \]

### Step 4: Set up the equation for total weight
The total weight of all students is the sum of the total weight of boys and the total weight of girls:

\[ A = \text{Total Weight of Boys} + \text{Total Weight of Girls} \]

Substituting the known values:

\[ 660 = 420 + 8y \]

### Step 5: Solve for \( y \)
Now, we can solve for \( y \):

1. Subtract 420 from both sides:

\[ 660 - 420 = 8y \]

\[ 240 = 8y \]

2. Divide both sides by 8:

\[ y = \frac{240}{8} = 30 \, \text{kg} \]

### Final Answer
The average weight of the 8 girls is \( y = 30 \, \text{kg} \).

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