To solve the problem step by step, let's break down the information provided and calculate the required values.
### Step 1: Understand the total number of employees
We know that the total number of males in all departments is 80.
### Step 2: Define the ratio for HR, Marketing, and Finance
The ratio of employees (male + female) in HR, Marketing, and Finance is given as 3:4:5.
Let the number of employees in HR = 3x, in Marketing = 4x, and in Finance = 5x.
### Step 3: Calculate total employees in HR, Marketing, and Finance
The total number of employees in HR, Marketing, and Finance can be expressed as:
\[
3x + 4x + 5x = 12x
\]
### Step 4: Information about females in HR and Marketing
We are told that there are 21 females in HR and Marketing together, which is 35% of the total number of females in all four departments. Let the total number of females in all departments be \( F \). Therefore:
\[
0.35F = 21 \implies F = \frac{21}{0.35} = 60
\]
### Step 5: Find the number of females in HR and Marketing
Let the number of females in HR be \( h \) and in Marketing be \( m \). We know:
1. \( h + m = 21 \)
2. \( m = h + 3 \)
Substituting the second equation into the first:
\[
h + (h + 3) = 21 \implies 2h + 3 = 21 \implies 2h = 18 \implies h = 9
\]
Thus, the number of females in HR is 9, and in Marketing:
\[
m = h + 3 = 9 + 3 = 12
\]
### Step 6: Calculate the number of females in Finance
The total number of females is 60. Therefore, the number of females in Finance is:
\[
F_f = 60 - (h + m) = 60 - (9 + 12) = 60 - 21 = 39
\]
### Step 7: Find the total number of employees in IT
We know there are 44 employees in the IT department. Also, 35% of the males are in IT:
\[
0.35 \times 80 = 28 \text{ males in IT}
\]
Thus, the number of females in IT is:
\[
44 - 28 = 16
\]
### Step 8: Calculate the total number of employees in all departments
Now, we can find the total number of employees:
\[
\text{Total employees} = \text{HR} + \text{Marketing} + \text{Finance} + \text{IT}
\]
\[
= (3x + 4x + 5x + 44) = 12x + 44
\]
### Step 9: Find the value of x
We know that the total number of males (80) is distributed as follows:
- Males in HR = \( \frac{3}{12} \times 80 = 20 \)
- Males in Marketing = \( \frac{4}{12} \times 80 = 26.67 \) (not possible, so we need to adjust)
- Males in Finance = \( \frac{5}{12} \times 80 = 33.33 \) (not possible, so we need to adjust)
Instead, we can find the total number of employees:
\[
12x + 44 = 140 \implies 12x = 140 - 44 = 96 \implies x = 8
\]
### Step 10: Calculate the number of employees in Finance
Now substituting \( x \):
\[
\text{Employees in Finance} = 5x = 5 \times 8 = 40
\]
### Step 11: Calculate the total number of employees
The total number of employees in all departments is:
\[
12x + 44 = 12 \times 8 + 44 = 96 + 44 = 140
\]
### Step 12: Find the percentage of employees in Finance
Now, we can find the percentage of employees in Finance:
\[
\text{Percentage} = \left( \frac{\text{Employees in Finance}}{\text{Total Employees}} \right) \times 100 = \left( \frac{40}{140} \right) \times 100 = \frac{4000}{140} \approx 28.57\%
\]
### Final Answer
The number of employees in Finance is approximately **28.57%** of the total number of employees in all four departments.
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