There are 50 students in a class in which boys are 8 more than the girls. Average weight of all the students is 50.5 kg and the average weight of all the girls is 48.5 kg then find the average weight of all the boys.

Options

A. 39.5 years
B. 52 kg
C. 40.5 kg
D. 56 kg

Explanation

To solve the problem step by step, we will follow the information provided in the question and use basic algebra to find the average weight of the boys.

### Step 1: Define Variables
Let the number of girls be \( x \). According to the problem, the number of boys is \( x + 8 \).

### Step 2: Set Up the Equation for Total Students
The total number of students in the class is given as 50. Therefore, we can set up the equation:
\[ x + (x + 8) = 50 \]

### Step 3: Simplify the Equation
Combining like terms gives us:
\[ 2x + 8 = 50 \]

### Step 4: Solve for \( x \)
Subtract 8 from both sides:
\[ 2x = 50 - 8 \]
\[ 2x = 42 \]
Now, divide by 2:
\[ x = 21 \]

### Step 5: Find the Number of Boys and Girls
From our definition:
- Number of girls = \( x = 21 \)
- Number of boys = \( x + 8 = 21 + 8 = 29 \)

### Step 6: Calculate Total Weight of All Students
The average weight of all students is given as 50.5 kg. Therefore, the total weight of all students can be calculated as:
\[ \text{Total weight of all students} = \text{Average weight} \times \text{Total number of students} \]
\[ \text{Total weight} = 50.5 \times 50 = 2525 \text{ kg} \]

### Step 7: Calculate Total Weight of Girls
The average weight of girls is given as 48.5 kg. Therefore, the total weight of all girls can be calculated as:
\[ \text{Total weight of girls} = \text{Average weight of girls} \times \text{Number of girls} \]
\[ \text{Total weight of girls} = 48.5 \times 21 = 1018.5 \text{ kg} \]

### Step 8: Calculate Total Weight of Boys
To find the total weight of the boys, we subtract the total weight of the girls from the total weight of all students:
\[ \text{Total weight of boys} = \text{Total weight of all students} - \text{Total weight of girls} \]
\[ \text{Total weight of boys} = 2525 - 1018.5 = 1506.5 \text{ kg} \]

### Step 9: Calculate Average Weight of Boys
Finally, we can find the average weight of the boys by dividing the total weight of boys by the number of boys:
\[ \text{Average weight of boys} = \frac{\text{Total weight of boys}}{\text{Number of boys}} \]
\[ \text{Average weight of boys} = \frac{1506.5}{29} \approx 51.2 \text{ kg} \]

### Final Answer
The average weight of all the boys is approximately **51.2 kg**.