Answer :
Answer:
To determine the percentage of students who are not scholarship holders, given the ratios and percentages, follow these steps:
### 1. Ratio of Boys and Girls
The ratio of boys to girls is \( 3:2 \).
Let:
- Number of boys = \( 3x \)
- Number of girls = \( 2x \)
### 2. Total Number of Students
Total students = \( 3x + 2x = 5x \)
### 3. Scholarship Holders
- **Boys**: 20% of \( 3x \) are scholarship holders.
\[
\text{Scholarship Boys} = 0.2 \times 3x = 0.6x
\]
- **Girls**: 30% of \( 2x \) are scholarship holders.
\[
\text{Scholarship Girls} = 0.3 \times 2x = 0.6x
\]
### 4. Total Scholarship Holders
\[
\text{Total Scholarship Holders} = 0.6x + 0.6x = 1.2x
\]
### 5. Students Not Holding Scholarships
Total students not holding scholarships:
\[
\text{Non-Scholarship Students} = \text{Total Students} - \text{Scholarship Holders} = 5x - 1.2x = 3.8x
\]
### 6. Percentage of Non-Scholarship Students
To find the percentage of students who are not scholarship holders:
\[
\text{Percentage} = \left( \frac{\text{Non-Scholarship Students}}{\text{Total Students}} \right) \times 100
\]
\[
\text{Percentage} = \left( \frac{3.8x}{5x} \right) \times 100 = \frac{3.8}{5} \times 100 = 76\%
\]
### Conclusion
The percentage of students who are not scholarship holders is \( \boxed{76\%} \).
So, the correct answer is (d) 76%.
Answer:
To find the percentage of students who are not scholarship holders, we'll start by breaking down the given information:
1. The ratio of boys to girls in the school is 3:2.
2. 20% of the boys are scholarship holders.
3. 30% of the girls are scholarship holders.
Let's assume the total number of students in the school is \(100\). This simplifies our calculations and will allow us to find the percentage more easily.
### Step 1: Calculate the number of boys and girls
Given the ratio of boys to girls is 3:2, we can use the ratio to divide the total number of students:
- Number of boys = \(\frac{3}{3+2} \times 100 = \frac{3}{5} \times 100 = 60\)
- Number of girls = \(\frac{2}{3+2} \times 100 = \frac{2}{5} \times 100 = 40\)
### Step 2: Calculate the number of scholarship holders
- Number of scholarship holder boys = 20% of 60 = \(0.20 \times 60 = 12\)
- Number of scholarship holder girls = 30% of 40 = \(0.30 \times 40 = 12\)
### Step 3: Calculate the total number of scholarship holders
Total number of scholarship holders = Number of scholarship holder boys + Number of scholarship holder girls = \(12 + 12 = 24\)
### Step 4: Calculate the number of students who are not scholarship holders
Total number of students who are not scholarship holders = Total number of students - Total number of scholarship holders = \(100 - 24 = 76\)
### Step 5: Calculate the percentage of students who are not scholarship holders
\[
\text{Percentage of students who are not scholarship holders} = \frac{76}{100} \times 100\% = 76\%
\]
Therefore, the percentage of the students who are not scholarship holders is \( \boxed{76\%} \).