The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

Options

A. 40
B. 20
C. 80
D. 60

Explanation

To solve the problem, we need to find the percentage of boys in a class where the average marks of boys is 52, the average marks of girls is 42, and the combined average is 50. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( x \) = number of boys
- \( y \) = number of girls

### Step 2: Write the Equation for Combined Average
The combined average of boys and girls can be expressed as:
\[ \frac{52x + 42y}{x + y} = 50 \]

### Step 3: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives:
\[ 52x + 42y = 50(x + y) \]

### Step 4: Expand the Right Side
Expanding the right side:
\[ 52x + 42y = 50x + 50y \]

### Step 5: Rearrange the Equation
Rearranging the equation to group like terms:
\[ 52x + 42y - 50x - 50y = 0 \]
This simplifies to:
\[ 2x - 8y = 0 \]

### Step 6: Solve for x in terms of y
From the equation \( 2x = 8y \), we can solve for \( x \):
\[ x = 4y \]

### Step 7: Calculate the Total Number of Students
The total number of students in the class is:
\[ x + y = 4y + y = 5y \]

### Step 8: Calculate the Percentage of Boys
The percentage of boys in the class can be calculated using the formula:
\[ \text{Percentage of boys} = \left( \frac{x}{x + y} \right) \times 100 \]
Substituting \( x = 4y \):
\[ \text{Percentage of boys} = \left( \frac{4y}{5y} \right) \times 100 \]

### Step 9: Simplify the Expression
This simplifies to:
\[ \text{Percentage of boys} = \left( \frac{4}{5} \right) \times 100 = 80\% \]

### Final Answer
The percentage of boys in the class is **80%**.

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