In an examination out of 480 students, 85% of the girls and 70% of the boys have passed.
How many boys appeared in the examination , if total pass percentage was 75% ?

Options

A. 370
B. 340
C. 320
D. 360

Explanation

To solve the problem, we need to find out how many boys appeared in the examination given the total number of students, the passing percentages of boys and girls, and the overall passing percentage. Here's a step-by-step solution:

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

From the problem, we know that the total number of students is:
\[ b + g = 480 \]

### Step 2: Express Girls in Terms of Boys
From the equation above, we can express the number of girls in terms of boys:
\[ g = 480 - b \]

### Step 3: Calculate the Total Number of Passes
We know the passing percentages:
- 85% of girls passed
- 70% of boys passed

The total number of students who passed the examination is given by the overall pass percentage:
\[ \text{Total Passes} = 75\% \text{ of } 480 = 0.75 \times 480 = 360 \]

### Step 4: Set Up the Equation for Total Passes
Now, we can express the total number of passes in terms of boys and girls:
\[ \text{Total Passes} = \text{Passes by Girls} + \text{Passes by Boys} \]
\[ 360 = 0.85g + 0.70b \]

### Step 5: Substitute for Girls
Substituting \( g \) from Step 2 into the equation:
\[ 360 = 0.85(480 - b) + 0.70b \]

### Step 6: Simplify the Equation
Now, distribute and simplify:
\[ 360 = 0.85 \times 480 - 0.85b + 0.70b \]
\[ 360 = 408 - 0.15b \]

### Step 7: Solve for Boys
Rearranging the equation to solve for \( b \):
\[ 0.15b = 408 - 360 \]
\[ 0.15b = 48 \]
\[ b = \frac{48}{0.15} \]
\[ b = 320 \]

### Step 8: Find the Number of Girls
Now, we can find the number of girls:
\[ g = 480 - b = 480 - 320 = 160 \]

### Conclusion
Thus, the number of boys who appeared in the examination is **320**.

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