Calculating Total Male Teachers in University

This problem asks us to find the total number of male teachers in a university based on a table showing the percentage distribution of teachers across different subjects and the ratio of male to female teachers within each subject. We are given that the total number of teachers in the university is 1600.

Analyzing the Provided Teacher Data

The table contains the following information:

Total number of teachers = 1600.

Step-by-Step Calculation of Male Teachers per Subject

To find the total number of male teachers, we first need to calculate the number of teachers in each subject and then determine the number of male teachers in that subject using the given ratio.

1. Calculate the Number of Teachers in Each Subject:

• Subject A: $13\%$ of $1600 = \frac{13}{100} \times 1600 = 13 \times 16 = 208$
• Subject B: $18\%$ of $1600 = \frac{18}{100} \times 1600 = 18 \times 16 = 288$
• Subject C: $12\%$ of $1600 = \frac{12}{100} \times 1600 = 12 \times 16 = 192$
• Subject D: $21\%$ of $1600 = \frac{21}{100} \times 1600 = 21 \times 16 = 336$
• Subject E: $14\%$ of $1600 = \frac{14}{100} \times 1600 = 14 \times 16 = 224$
• Subject F: $22\%$ of $1600 = \frac{22}{100} \times 1600 = 22 \times 16 = 352$

2. Calculate the Number of Male Teachers in Each Subject:

Using the male:female ratio for each subject, we can find the number of male teachers. The ratio a:b means that for every (a+b) teachers, 'a' are male and 'b' are female. The fraction of male teachers is $\frac{a}{a+b}$.

• Subject A: Ratio 1:7. Total parts = $1+7=8$. Male teachers = $\frac{1}{8} \times 208 = 26$.
• Subject B: Ratio 5:3. Total parts = $5+3=8$. Male teachers = $\frac{5}{8} \times 288 = 5 \times 36 = 180$.
• Subject C: Ratio 1:3. Total parts = $1+3=4$. Male teachers = $\frac{1}{4} \times 192 = 48$.
• Subject D: Ratio 3:4. Total parts = $3+4=7$. Male teachers = $\frac{3}{7} \times 336 = 3 \times 48 = 144$.
• Subject E: Ratio 9:5. Total parts = $9+5=14$. Male teachers = $\frac{9}{14} \times 224 = 9 \times 16 = 144$.
• Subject F: Ratio 7:9. Total parts = $7+9=16$. Male teachers = $\frac{7}{16} \times 352 = 7 \times 22 = 154$.

3. Calculate the Total Number of Male Teachers:

Sum the number of male teachers from all subjects:

Total Male Teachers = Male (A) + Male (B) + Male (C) + Male (D) + Male (E) + Male (F)

Total Male Teachers = $26 + 180 + 48 + 144 + 144 + 154 = 696$.

Summary of Male and Female Teachers by Subject

Conclusion

The total number of male teachers in the University is 696.

Revision Table - University Staff Data Calculation

This section summarizes the key values calculated during the process of finding the total male teachers.

Additional Information - Data Interpretation Skills

Data interpretation questions like this one test your ability to extract, calculate, and analyze information presented in tables or graphs. Key skills involved include:

• Reading and Understanding Data: Carefully understanding what the rows, columns, and headings in the table represent.
• Percentage Calculations: Applying percentage formulas to find parts of a whole.
• Ratio and Proportion: Using ratios to divide quantities into proportional parts.
• Arithmetic Operations: Performing addition, multiplication, and division accurately.
• Organized Calculation: Breaking down the problem into smaller, manageable steps, such as calculating values for each subject separately before summing up.

Practicing with different types of data tables and charts is essential for improving data interpretation skills for exams.