Calculating Male to Female Student Ratio in College D

The question asks us to find the ratio of the total number of male students to the total number of female students in College D, based on the provided table data. The table gives us the pass percentage and the ratio of male to female students among both passed and failed students for different colleges.

Understanding the Data for College D

Let's extract the relevant information for College D from the table:

• Pass percentage in College D = 45%
• Ratio of Male to Female students among passed students in College D = 4 ∶ 1
• Ratio of Male to Female students among failed students in College D = 7 ∶ 3

From the pass percentage, we can determine the fail percentage. If 45% of students passed, then 100% - 45% = 55% of students failed.

Step-by-Step Calculation of Male and Female Students in College D

Let's assume the total number of students in College D is \( T \). While we don't need the exact number, using a variable helps represent the proportions correctly. The final ratio will be independent of the total number of students.

1. Calculate the number of passed and failed students:

• Number of passed students = 45% of \( T = 0.45T \)
• Number of failed students = 55% of \( T = 0.55T \)

2. Calculate the number of male and female students among passed students:

The ratio of Male to Female among passed students is 4 ∶ 1. This means that for every 4 male students who passed, there is 1 female student who passed. The parts in this ratio sum up to \( 4 + 1 = 5 \).

• Number of male students who passed = \( \frac{4}{5} \) of (Number of passed students) = \( \frac{4}{5} \times 0.45T = 4 \times 0.09T = 0.36T \)
• Number of female students who passed = \( \frac{1}{5} \) of (Number of passed students) = \( \frac{1}{5} \times 0.45T = 1 \times 0.09T = 0.09T \)

3. Calculate the number of male and female students among failed students:

The ratio of Male to Female among failed students is 7 ∶ 3. The parts in this ratio sum up to \( 7 + 3 = 10 \).

• Number of male students who failed = \( \frac{7}{10} \) of (Number of failed students) = \( \frac{7}{10} \times 0.55T = 7 \times 0.055T = 0.385T \)
• Number of female students who failed = \( \frac{3}{10} \) of (Number of failed students) = \( \frac{3}{10} \times 0.55T = 3 \times 0.055T = 0.165T \)

4. Calculate the total number of male and female students in College D:

• Total number of male students in College D = (Male passed) + (Male failed) = \( 0.36T + 0.385T = 0.745T \)
• Total number of female students in College D = (Female passed) + (Female failed) = \( 0.09T + 0.165T = 0.255T \)

5. Find the ratio of total male to total female students:

The ratio of male to female students is the total number of male students divided by the total number of female students.

\( \text{Ratio} = \frac{\text{Total Male Students}}{\text{Total Female Students}} = \frac{0.745T}{0.255T} \)

The \( T \) cancels out, as expected. We are left with the ratio \( 0.745 : 0.255 \).

To express this ratio as whole numbers, we can multiply both sides by 1000:

\( 0.745 \times 1000 : 0.255 \times 1000 = 745 : 255 \)

Now, we simplify the ratio \( 745 : 255 \) by finding the greatest common divisor (GCD). Both numbers end in 5, so they are divisible by 5.

• \( 745 \div 5 = 149 \)
• \( 255 \div 5 = 51 \)

So, the simplified ratio is \( 149 : 51 \).

We should check if 149 and 51 have any common factors other than 1. 51 is \( 3 \times 17 \). We can check if 149 is divisible by 3 or 17. The sum of digits of 149 is \( 1+4+9 = 14 \), which is not divisible by 3, so 149 is not divisible by 3. \( 17 \times 8 = 136 \), \( 17 \times 9 = 153 \). So, 149 is not divisible by 17. Thus, 149 and 51 are coprime, and the ratio \( 149 : 51 \) is in its simplest form.

Final Answer Derivation

The ratio of the number of male students to the number of female students in College D is \( 149 : 51 \).

Revision Table: College D Student Ratios

The total male to female ratio is \( 0.745T : 0.255T \), which simplifies to \( 149 : 51 \).

Additional Information: Understanding Ratios and Percentages in Data Interpretation

Data interpretation questions often involve combining information presented in different formats, such as percentages and ratios. To solve such problems effectively:

• Percentages: Represent parts of a whole out of 100. A percentage can be easily converted into a decimal or a fraction for calculations (e.g., 45% = 0.45 = 45/100).
• Ratios: Express the relative size of two or more values (e.g., 4 ∶ 1). The sum of the parts in a ratio represents the total number of units for that category (e.g., in a 4 ∶ 1 ratio, there are 4+1=5 total parts). To find the value of one part, divide the total quantity for that category by the sum of the ratio parts.
• Combining Data: When combining percentages and ratios, it's often helpful to think in terms of proportions relative to a total quantity. Assuming a base value (like the total number of students \( T \)) or even a specific number (like 100 or 1000 if it simplifies calculations) can make the process clearer. The key is to maintain consistency across calculations.
• Simplifying Ratios: Always simplify ratios to their lowest terms by dividing all parts by their greatest common divisor.

These techniques are fundamental for solving data interpretation questions involving population distributions, survey results, financial statements, and academic performance data like the one presented here.