In a class of 80 students. 60% are girls and the rest are boys. The average weight of boys is 5% more than that of girls. If the average weight of all the student is 51 kg, then what is the average weight (in kg) of the boys?

Options

A. 47.5
B. 55
C. 52.5
D. 50

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Determine the number of girls and boys in the class.
- Total students = 80
- Percentage of girls = 60%
- Number of girls = 60% of 80 = (60/100) * 80 = 48
- Number of boys = Total students - Number of girls = 80 - 48 = 32

**Hint:** To find the number of girls and boys, use the percentage to calculate the number of girls and subtract from the total to find the boys.

### Step 2: Set up the average weight relationship.
- Let the average weight of girls be \( G \) kg.
- The average weight of boys is 5% more than that of girls, so:
\[ B = G + 0.05G = 1.05G \]
where \( B \) is the average weight of boys.

**Hint:** Remember that "5% more" means you add 5% of the original value to itself.

### Step 3: Use the average weight of all students.
- The average weight of all students is given as 51 kg.
- The total weight of girls = Number of girls * Average weight of girls = \( 48G \)
- The total weight of boys = Number of boys * Average weight of boys = \( 32B \)
- The average weight of all students can be expressed as:
\[ \frac{48G + 32B}{80} = 51 \]

**Hint:** The formula for average weight is the total weight divided by the number of students.

### Step 4: Substitute \( B \) in the average weight equation.
- Substitute \( B \) with \( 1.05G \):
\[ \frac{48G + 32(1.05G)}{80} = 51 \]
- Simplifying this gives:
\[ \frac{48G + 33.6G}{80} = 51 \]
\[ \frac{81.6G}{80} = 51 \]

**Hint:** When substituting, ensure you distribute correctly and combine like terms.

### Step 5: Solve for \( G \).
- Multiply both sides by 80:
\[ 81.6G = 51 \times 80 \]
\[ 81.6G = 4080 \]
- Now, divide by 81.6 to find \( G \):
\[ G = \frac{4080}{81.6} = 50 \]

**Hint:** To isolate \( G \), perform the inverse operation of multiplication.

### Step 6: Calculate the average weight of boys \( B \).
- Now that we have \( G \), substitute back to find \( B \):
\[ B = 1.05G = 1.05 \times 50 = 52.5 \]

**Hint:** Use the relationship established earlier to find the average weight of boys.

### Final Answer:
The average weight of the boys is **52.5 kg**.