Exploring the Scholarship Distribution among Students in Different Gender Proportions

A balanced distribution of educational resources is crucial for ensuring equal opportunities for all students. This article delves into the distribution of scholarships among students based on different gender proportions, providing a detailed analysis of each scenario.

1. Boys and Girls in a 8:12 Ratio

The ratio of the number of boys to girls in a school is 8:12. If 50 boys and 25 girls receive scholarships, we aim to find the percentage of students who do not receive any scholarships.

Calculation Steps:

Let: Number of Boys 3x, Number of Girls 2x, Total Number of Students 5x Boys Receiving Scholarships: 50 (which is 0.6 of 3x) 0.6x Girls Receiving Scholarships: 25 (which is 0.3 of 2x) 0.6x Total Students Receiving Scholarships: 0.6x 0.6x 1.2x Total Students Not Receiving Scholarships: 5x - 1.2x 3.8x Percentage Calculation: (3.8x / 5x) x 100 76%

Therefore, 76% of the school students are not getting any scholarships.

2. Boys and Girls in a 3:2 Ratio

Suppose the ratio of the number of students in a class is 3:2, where boys are 60 and girls are 40. If 20 boys and 30 girls receive scholarships, we can calculate the percentage of students who do not receive any scholarships.

Calculation Steps:

Number of Boys 60, Number of Girls 40 Boys Receiving Scholarships: 20 (which is 40% of 60) 0.4 x 60 24 Girls Receiving Scholarships: 30 (which is 75% of 40) 0.75 x 40 30 Total Students Receiving Scholarships: 24 30 54 Total Students Not Receiving Scholarships: 100 - 54 46

Therefore, 46 students out of 100 are not getting any scholarships. This effectively translates to 46%.

3. Boys and Girls in a 3:4 Ratio

Let us now consider the scenario where the ratio of boys to girls is 3:4, and a total of 100 students. If 50 boys and 25 girls receive scholarships, we can calculate the percentage of students who do not receive any scholarships.

Calculation Steps:

Number of Boys 3x, Number of Girls 4x, Total Number of Students 7x (since x 100) Boys Receiving Scholarships: 50 (which is 50% of 100) 0.5 x 100 50 Girls Receiving Scholarships: 25 (which is 25% of 100) 0.25 x 100 25 Total Students Receiving Scholarships: 50 25 75 Total Students Not Receiving Scholarships: 100 - 75 25

Therefore, 25 students out of 100 are not getting any scholarships. This effectively translates to 25%.

4. Generalized Case: B:G Ratio Example

Given the ratio B:G 3:2. Let the number of students be B 3S and G 2S, then the total number of students is 5S. Assuming that 0.4B and 0.2G students receive scholarships:

Number of Boys Receiving Scholarships: 0.4 x 3S 1.2S Number of Girls Receiving Scholarships: 0.2 x 2S 0.4S Total Students Receiving Scholarships: 1.2S 0.4S 1.6S Total Students Not Receiving Scholarships: 5S - 1.6S 3.4S Percentage Calculation: (3.4S / 5S) x 100 68%

Therefore, 68% of the students are not getting any scholarships.

Through these detailed calculations, we can see the impact of varying student ratios on the distribution of scholarships. Each scenario provides unique insights into optimizing equal educational opportunities for all students.