Question

The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000. 
The total number of management degree holders among the executives in companies C2 and C5 together is 

• A. 225
• B. 600
• C. 1900
• D. 2500

Hint:

When dealing with percentage distributions, ensure you first calculate the exact number of executives in each company before applying the ratio for management degree holders.

Answer 1

The Correct Option is C

We are given the following information:
- The total number of executives across all companies is 10,000.
- The percentage distribution of employees across the companies is:
- \( C1: 15% \)
- \( C2: 5% \)
- \( C3: 8% \)
- \( C4: 32% \)
- \( C5: 20% \)
- \( C6: 20% \)
Step 1: Calculate the number of executives in each company
The number of executives in each company is:
- Number of executives in \( C1 = 15% \times 10,000 = 1500 \)
- Number of executives in \( C2 = 5% \times 10,000 = 500 \)
- Number of executives in \( C3 = 8% \times 10,000 = 800 \)
- Number of executives in \( C4 = 32% \times 10,000 = 3200 \)
- Number of executives in \( C5 = 20% \times 10,000 = 2000 \)
- Number of executives in \( C6 = 20% \times 10,000 = 2000 \)
Step 2: Calculate the number of management degree holders in \( C2 \) and \( C5 \) - For \( C2 \), the ratio of executives with a management degree is \( 1:4 \), meaning 1 out of every 5 executives has a management degree. \[ \text{Management degree holders in } C2 = \frac{1}{5} \times 500 = 100 \] - For \( C5 \), the ratio of executives with a management degree is \( 9:1 \), meaning 9 out of every 10 executives have a management degree. \[ \text{Management degree holders in } C5 = \frac{9}{10} \times 2000 = 1800 \] Step 3: Total management degree holders in \( C2 \) and \( C5 \) The total number of management degree holders in \( C2 \) and \( C5 \) together is: \[ 100 + 1800 = 1900 \] Thus, the total number of management degree holders in companies \( C2 \) and \( C5 \) is 1900, corresponding to Option (C).
Final Answer: (C) 1900