The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 30% of the girls are scholarship holders, then the percentage of students, who do not get scholarship, is

Options

A. 50
B. 72
C. 75
D. 76

Answer

To solve the problem, we need to find the percentage of students who do not receive a scholarship based on the given ratio of boys to girls and the percentages of scholarship holders among them.

### Step-by-Step Solution:

1. **Identify the Ratios**:
- The ratio of boys to girls is given as 3:2.
- Let the number of boys be \(3x\) and the number of girls be \(2x\).

2. **Calculate the Total Number of Students**:
- Total students = Number of boys + Number of girls = \(3x + 2x = 5x\).

3. **Calculate the Number of Scholarship Holders**:
- **Boys**: 20% of boys are scholarship holders.
\[ \text{Number of boys with scholarship} = 20\% \text{ of } 3x = \frac{20}{100} \times 3x = 0.6x \]
- **Girls**: 30% of girls are scholarship holders.
\[ \text{Number of girls with scholarship} = 30\% \text{ of } 2x = \frac{30}{100} \times 2x = 0.6x \]

4. **Calculate the Total Number of Scholarship Holders**:
- Total scholarship holders = Number of boys with scholarship + Number of girls with scholarship
\[ \text{Total scholarship holders} = 0.6x + 0.6x = 1.2x \]

5. **Calculate the Number of Students without Scholarship**:
- Total students without scholarship = Total students - Total scholarship holders
\[ \text{Students without scholarship} = 5x - 1.2x = 3.8x \]

6. **Calculate the Percentage of Students without Scholarship**:
- Percentage of students without scholarship =
\[ \left(\frac{\text{Students without scholarship}}{\text{Total students}}\right) \times 100 = \left(\frac{3.8x}{5x}\right) \times 100 = \frac{3.8}{5} \times 100 = 76\% \]

### Final Answer:
The percentage of students who do not get a scholarship is **76%**.