Analyzing Company Employee Distribution

The question asks us to determine the number of graduate employees in department C as a percentage of the number of Post-Graduate employees working in department E. We are provided with the total number of employees, ratios of male to female and graduate to post-graduate, and the percentage distribution of employees, males, and graduates across six departments (A-F).

Understanding the Given Data

We have the following key information:

• Total number of employees = 8000
• Ratio of Male to Female employees = 3 ∶ 5
• Ratio of Graduate to Post-Graduate employees = 3 ∶ 2
• A table showing the percentage distribution by department for Employees, Males, and Graduates.

Step-by-Step Calculation

1. Calculate Total Number of Graduates and Post-Graduates

The total number of employees is 8000. The ratio of Graduate to Post-Graduate employees is 3 ∶ 2. This means that out of every 5 employees, 3 are graduates and 2 are post-graduates.

• Total ratio parts for graduates and post-graduates = \(3 + 2 = 5\)
• Total number of Graduates = \(\left(\frac{3}{5}\right) \times 8000 = 3 \times 1600 = 4800\)
• Total number of Post-Graduates = \(\left(\frac{2}{5}\right) \times 8000 = 2 \times 1600 = 3200\)

2. Calculate Number of Graduate Employees in Department C

From the table, 13% of the total graduates work in department C. We know the total number of graduates is 4800.

• Number of Graduates in Department C = \(13\% \text{ of } 4800\)
• Number of Graduates in Department C = \(\left(\frac{13}{100}\right) \times 4800 = 13 \times 48 = 624\)

So, there are 624 graduate employees in department C.

3. Calculate Number of Employees in Department E

From the table, 15% of the total employees work in department E. We know the total number of employees is 8000.

• Number of Employees in Department E = \(15\% \text{ of } 8000\)
• Number of Employees in Department E = \(\left(\frac{15}{100}\right) \times 8000 = 15 \times 80 = 1200\)

So, there are 1200 total employees in department E.

4. Calculate Number of Graduate Employees in Department E

From the table, 20% of the total graduates work in department E. We know the total number of graduates is 4800.

• Number of Graduates in Department E = \(20\% \text{ of } 4800\)
• Number of Graduates in Department E = \(\left(\frac{20}{100}\right) \times 4800 = 20 \times 48 = 960\)

So, there are 960 graduate employees in department E.

5. Calculate Number of Post-Graduate Employees in Department E

The total employees in department E consist of graduates and post-graduates. We know the total employees in E (1200) and the graduates in E (960).

• Number of Post-Graduates in Department E = (Total Employees in E) - (Number of Graduates in E)
• Number of Post-Graduates in Department E = \(1200 - 960 = 240\)

So, there are 240 post-graduate employees in department E.

6. Calculate the Required Percentage

We need to find the number of graduate employees working in department C as a percentage of the number of Post-Graduate employees working in department E.

• Required Percentage = \(\left(\frac{\text{Number of Graduates in Department C}}{\text{Number of Post-Graduates in Department E}}\right) \times 100\)
• Required Percentage = \(\left(\frac{624}{240}\right) \times 100\)
• Required Percentage = \(\left(\frac{624}{24}\right) \times 10\)
• Required Percentage = \(26 \times 10 = 260\)

Thus, the number of graduate employees working in department C is 260% of the number of Post-Graduate employees working in department E.

Revision Table: Employee Data Analysis

Additional Information: Ratio and Percentage Concepts

This problem involves understanding how to work with ratios and percentages in the context of data distribution. A ratio like 3 ∶ 5 tells us the proportion of different groups within a total. For example, in the Male to Female ratio of 3 ∶ 5, for every 3 males, there are 5 females, making a total of \(3+5=8\) parts. Percentages represent a fraction out of 100, allowing us to easily scale proportions to any total number. When a table shows percentage distributions across categories (like departments), these percentages apply to the relevant total (e.g., percentage of employees in a department is based on the total number of employees, percentage of graduates in a department is based on the total number of graduates).

To find the number of individuals in a specific category (e.g., post-graduates in department E), we sometimes need to use multiple pieces of information. In this case, total employees in department E include both graduates and post-graduates within that department. By finding the total employees in E and the graduates in E, we can subtract to find the post-graduates in E.

Calculating one number as a percentage of another involves the formula: \(\left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\). Here, the "Part" is the number of graduates in department C, and the "Whole" is the number of post-graduates in department E.