Calculating the Pass Percentage in a Class With a Specific Gender Ratio

This article delves into a specific problem involving a class with a gender ratio and explores how to calculate the pass percentage of students. We will solve the problem mathematically and present the results in a format that is easier to understand. Additionally, we include a C program to verify our calculations.

Problem Statement

Consider a class where the ratio of the number of boys to the number of girls is 11:9. Among these students, 30 boys and 20 girls have passed. What is the percentage of the class that passed the exam?

Mathematical Solution

Let's denote the number of boys as B and the number of girls as G. According to the given ratio, the number of boys and girls can be expressed as:

B : G 11 : 9

First, let's assume the total number of students is 60, the smallest number where both boys and girls will pass or fail as whole numbers.

Step 1: Determine the Number of Boys and Girls

From the ratio, we can write:

B ( frac{11}{20} ) of total students G ( frac{9}{20} ) of total students

For a total of 60 students:

B ( frac{11}{20} ) * 60 33 boys G ( frac{9}{20} ) * 60 27 girls

Step 2: Calculate the Number of Failures and Passes

Given:

Number of boys who passed 30 Number of girls who passed 20

Number of boys who failed 30 - (30/100) * 33 30 - 10 20 Number of girls who failed 20 - (20/100) * 27 20 - 5.4 ≈ 15 (considering whole numbers)

Total number of failures 20 boys 15 girls 35

Total number of passes 60 - 35 25

Percentage Calculation

The pass percentage is calculated as follows:

Pass percentage ( frac{25}{60} ) * 100 41.67%

Verification Using a C Program

Here is a C program that verifies the calculations:

include math.hinclude stdio.hint main(void) {    double f  1.0;    double num_b  0.0;    double num_g  0.0;    double b_fail  0.0;    double b_pass  0.0;    double g_fail  0.0;    double g_pass  0.0;    double b_frac  0.0;    double g_frac  0.0;    double temp  0.0;    double total_pass  0.0;    double percent  0.0;    // Iterate through multiples of 60 for sensible results    while (f 

Conclusion

The calculations show that the pass percentage of the class is approximately 41.67%. This result is confirmed by the C program, which iterates through the multiples of 60 to find the smallest class size where all passing and failing numbers are whole numbers.

Related Keywords

class ratio pass percentage gender ratio

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