Calculating Male Student Pass Percentage in College A

The question asks for the pass percentage of male students in College A based on the provided data table. The table gives the overall pass percentage for College A and the ratio of male to female students among both the passed and failed groups.

Let's extract the relevant data for College A:

We are given the overall pass percentage for College A is 40%. This means 40% of the total students passed, and consequently, 60% failed.

The ratio of male to female students among those who passed is 12:13. This means for every 12 male students who passed, there were 13 female students who passed. The total number of parts in this ratio is $12 + 13 = 25$.

The ratio of male to female students among those who failed is 12:5. This means for every 12 male students who failed, there were 5 female students who failed. The total number of parts in this ratio is $12 + 5 = 17$.

The question asks for the "pass percentage of male students". Based on the options provided, this is interpreted as the percentage of the total number of students in College A who are male and have passed. Let's proceed with this interpretation.

Step-by-Step Calculation

Step 1: Assume a Total Number of Students

Let the total number of students in College A be $T$.

Step 2: Calculate the Number of Passed Students

Given the overall pass percentage is 40%, the number of students who passed is:

\( \text{Number of passed students} = 40\% \text{ of } T = \frac{40}{100} \times T = 0.4 T \)

Step 3: Calculate the Number of Male Students among Passed Students

Among the passed students, the ratio of Male to Female is 12:13. The proportion of male students among the passed students is $\frac{12}{12+13} = \frac{12}{25}$.

The number of male students who passed is:

\( \text{Number of male passed students} = \frac{12}{25} \times (\text{Number of passed students}) \)

\( \text{Number of male passed students} = \frac{12}{25} \times (0.4 T) \)

Calculate the fraction: \( \frac{12}{25} \times 0.4 = \frac{12}{25} \times \frac{4}{10} = \frac{12}{25} \times \frac{2}{5} = \frac{24}{125} \)

So, the number of male passed students is \( \frac{24}{125} T \).

Step 4: Calculate the Required Percentage

Under the assumed interpretation, the pass percentage of male students is the number of male passed students as a percentage of the total number of students:

\( \text{Pass percentage of male students} = \frac{\text{Number of male passed students}}{\text{Total number of students}} \times 100\% \)

\( \text{Pass percentage of male students} = \frac{\frac{24}{125} T}{T} \times 100\% \)

\( \text{Pass percentage of male students} = \frac{24}{125} \times 100\% \)

Step 5: Evaluate the Percentage

Now, calculate the value:

\( \frac{24}{125} \times 100 = \frac{24 \times 100}{125} \)

We can simplify this by dividing 100 and 125 by 25:

\( \frac{24 \times 4}{5} = \frac{96}{5} \)

To express $\frac{96}{5}$ as a mixed number or decimal:

\( \frac{96}{5} = 19 \frac{1}{5} \) (since $96 = 5 \times 19 + 1$)

or \( \frac{96}{5} = 19.2 \)

The pass percentage of male students in College A is $19 \frac{1}{5}\%$. This matches one of the given options.

Revision Table: College A Academic Data

• Overall Pass Percentage: 40%
• Overall Fail Percentage: 60%
• Ratio (Pass): Male : Female = 12 : 13
• Ratio (Fail): Male : Female = 12 : 5
• Calculated value: \( \frac{\text{Male Passed}}{\text{Total Students}} \times 100\% = 19 \frac{1}{5}\% \)

Additional Information: Interpreting Pass Percentage

In this problem, based on the options, "pass percentage of male students" was interpreted as the percentage of the total student population who are male and passed. However, another common interpretation of "pass percentage of male students" is the percentage of the total male students who passed the exam. Let's explore that briefly:

Number of male passed students = \( \frac{24}{125} T \)

Number of failed students = $60\%$ of $T = 0.6T$

Among failed students, ratio of Male:Female is 12:5. Proportion of male failed students = $\frac{12}{12+5} = \frac{12}{17}$.

Number of male failed students = \( \frac{12}{17} \times 0.6 T = \frac{12}{17} \times \frac{6}{10} T = \frac{12}{17} \times \frac{3}{5} T = \frac{36}{85} T \)

Total number of male students = Number of male passed + Number of male failed

\( \text{Total male students} = \frac{24}{125} T + \frac{36}{85} T \)

Find a common denominator for 125 ($5^3$) and 85 ($5 \times 17$). The least common multiple is $5^3 \times 17 = 125 \times 17 = 2125$.

\( \frac{24}{125} = \frac{24 \times 17}{125 \times 17} = \frac{408}{2125} \)

\( \frac{36}{85} = \frac{36 \times 25}{85 \times 25} = \frac{900}{2125} \)

\( \text{Total male students} = \left(\frac{408}{2125} + \frac{900}{2125}\right) T = \frac{1308}{2125} T \)

Under the alternative interpretation (Male Passed / Total Male * 100%):

\( \frac{\frac{408}{2125} T}{\frac{1308}{2125} T} \times 100\% = \frac{408}{1308} \times 100\% \)

Simplify the fraction $\frac{408}{1308}$ by dividing by common factors (e.g., 4, then 3):

\( \frac{408 \div 4}{1308 \div 4} = \frac{102}{327} \)

\( \frac{102 \div 3}{327 \div 3} = \frac{34}{109} \)

So, the percentage is \( \frac{34}{109} \times 100\% = \frac{3400}{109}\% \). As a mixed number, this is \( 31 \frac{21}{109}\% \), which is approximately 31.2%. This value is not among the given options, confirming the first interpretation was likely intended by the question setter.