The average pass percentage of girls in class XII examination in a school is 80 and that of boys is 75. The average pass percentage in class XII of that school is 76.5 Find the percentage of the number of boys in class XII of the school.

Options

A. 72
B. 60
C. 70
D. 65

Answer

To solve the problem step by step, we need to find the percentage of boys in class XII based on the given average pass percentages of girls and boys, and the overall average pass percentage.

### Step 1: Define Variables
Let:
- \( G \) = Number of girls
- \( B \) = Number of boys

### Step 2: Set Up the Equations
From the problem, we know:
- Average pass percentage of girls = 80%
- Average pass percentage of boys = 75%
- Overall average pass percentage = 76.5%

We can express the overall average pass percentage in terms of the number of girls and boys:
\[ \frac{80G + 75B}{G + B} = 76.5 \]

### Step 3: Clear the Denominator
Multiply both sides by \( G + B \):
\[ 80G + 75B = 76.5(G + B) \]

### Step 4: Expand the Equation
Expanding the right side gives:
\[ 80G + 75B = 76.5G + 76.5B \]

### Step 5: Rearrange the Equation
Rearranging terms to isolate \( G \) and \( B \):
\[ 80G - 76.5G = 76.5B - 75B \]
\[ 3.5G = 1.5B \]

### Step 6: Simplify the Ratio
Dividing both sides by \( 1.5 \):
\[ \frac{G}{B} = \frac{1.5}{3.5} = \frac{3}{7} \]

### Step 7: Find the Percentage of Boys
The ratio of boys to the total number of students (boys + girls) is:
\[ \text{Total} = G + B = 3x + 7x = 10x \]
Where \( x \) is a common factor.

The percentage of boys is:
\[ \text{Percentage of boys} = \frac{B}{G + B} \times 100 = \frac{7x}{10x} \times 100 = 70\% \]

### Final Answer
The percentage of the number of boys in class XII of the school is **70%**.

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