The ratio of the number of boys and girls In a school is `8 : 12`. If 50% of boys and 25% of girls are getting scholarships for their studies, what is the percentage of school students who are not getting any scholarships ?

Options

A. 65
B. 66
C. 67
D. 68

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript and clarify each step.

### Step 1: Understand the Ratio
The ratio of boys to girls in the school is given as 8:12. We can simplify this ratio to find the actual number of boys and girls.

**Calculation:**
- Simplifying the ratio 8:12 gives us:
- Divide both parts by 4:
- Boys = 8/4 = 2
- Girls = 12/4 = 3
- Thus, the simplified ratio is 2:3.

### Step 2: Assign Values to Boys and Girls
To make calculations easier, we can assign a common multiple to the ratio. Let's assume there are 20 boys and 30 girls (multiplying the simplified ratio by 10).

**Calculation:**
- Boys = 2 * 10 = 20
- Girls = 3 * 10 = 30

### Step 3: Calculate Total Students
Now, we can calculate the total number of students in the school.

**Calculation:**
- Total students = Boys + Girls = 20 + 30 = 50

### Step 4: Calculate Boys Getting Scholarships
Next, we need to find out how many boys are getting scholarships. It is given that 50% of boys receive scholarships.

**Calculation:**
- Boys getting scholarships = 50% of 20 = (50/100) * 20 = 10 boys

### Step 5: Calculate Boys Not Getting Scholarships
Now, we can find out how many boys are not getting scholarships.

**Calculation:**
- Boys not getting scholarships = Total boys - Boys getting scholarships = 20 - 10 = 10 boys

### Step 6: Calculate Girls Getting Scholarships
Next, we need to calculate how many girls are getting scholarships. It is given that 25% of girls receive scholarships.

**Calculation:**
- Girls getting scholarships = 25% of 30 = (25/100) * 30 = 7.5 girls

### Step 7: Calculate Girls Not Getting Scholarships
Now, we can find out how many girls are not getting scholarships.

**Calculation:**
- Girls not getting scholarships = Total girls - Girls getting scholarships = 30 - 7.5 = 22.5 girls

### Step 8: Calculate Total Students Not Getting Scholarships
We can now find the total number of students not getting scholarships by adding the boys and girls not receiving scholarships.

**Calculation:**
- Total students not getting scholarships = Boys not getting scholarships + Girls not getting scholarships = 10 + 22.5 = 32.5 students

### Step 9: Calculate the Percentage of Students Not Getting Scholarships
Finally, we need to calculate the percentage of students not getting scholarships out of the total number of students.

**Calculation:**
- Percentage of students not getting scholarships = (Total students not getting scholarships / Total students) * 100
- = (32.5 / 50) * 100 = 65%

### Final Answer
The percentage of school students who are not getting any scholarships is **65%**.

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