Study the following information carefully and answer the given questions.
Data regarding distribution of a certain number of employees (male `+` female) in four departments - HR, Marketing, Finance and IT—in 2015. The number of males (in all departments) is 80.
The ratio of the number of employees (male `+` female) in HR, Marketing and Finance is `3 : 4: 5`. There are total 21 females in HR and Marketing together, which is `35%` of the number of females (in all four departments). The number of females in Marketing is 3 more than that in HR.
There are 44 employees (male+female) in IT department. `35%` of male (in all four departments) are in this department.
What is the difference between the number of employees (male `+` female) in IT and the number of employees (male `+` female) in HR?

Options

A. 24
B. 22
C. 18
D. 20

Answer

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 Males
The total number of males across all departments is given as 80.

### Step 2: Set Up the Ratios for HR, Marketing, and Finance
The ratio of the number of employees (male + female) in HR, Marketing, and Finance is given as 3:4:5.
Let the number of employees in HR, Marketing, and Finance be represented as:
- HR = 3x
- Marketing = 4x
- Finance = 5x

### Step 3: Calculate Total Employees in HR, Marketing, and Finance
The total number of employees in HR, Marketing, and Finance combined is:
\[ 3x + 4x + 5x = 12x \]

### Step 4: Determine the Number of Females in HR and Marketing
We know that there are 21 females in HR and Marketing together, which is 35% of the total number of females in all departments. Let the total number of females be \( F \).

From the information given:
\[ 0.35F = 21 \]
To find \( F \):
\[ F = \frac{21}{0.35} = 60 \]

### Step 5: Find the Number of Females in HR and Marketing
Let the number of females in HR be \( a \) and in Marketing be \( a + 3 \). We know:
\[ a + (a + 3) = 21 \]
This simplifies to:
\[ 2a + 3 = 21 \]
\[ 2a = 18 \implies a = 9 \]
Thus, the number of females in HR is 9, and in Marketing is:
\[ 9 + 3 = 12 \]

### Step 6: Calculate the Number of Females in IT and Finance
Now we can find the number of females in Finance:
Total females = 60
Females in HR = 9
Females in Marketing = 12
Females in IT = 16 (as calculated later)
Thus, females in Finance:
\[ 60 - (9 + 12 + 16) = 60 - 37 = 23 \]

### Step 7: Calculate the Number of Employees in IT
It is given that there are 44 employees (male + female) in the IT department.
We also know that 35% of the total males (80) 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 Employees in Each Department
Now, we can summarize the total employees (male + female) in each department:
- HR: \( 3x \) (we will calculate \( x \) next)
- Marketing: \( 4x \)
- Finance: \( 5x \)
- IT: 44

### Step 9: Set Up the Equation for Total Employees
The total number of employees across all departments is:
\[ 3x + 4x + 5x + 44 = 140 \]
This simplifies to:
\[ 12x + 44 = 140 \]
\[ 12x = 96 \implies x = 8 \]

### Step 10: Calculate the Number of Employees in HR
Now we can calculate the number of employees in HR:
\[ HR = 3x = 3 \times 8 = 24 \]

### Step 11: Find the Difference Between IT and HR Employees
Finally, we need to find the difference between the number of employees in IT and HR:
\[ \text{Difference} = \text{Employees in IT} - \text{Employees in HR} = 44 - 24 = 20 \]

### Conclusion
The difference between the number of employees (male + female) in IT and HR is **20**.

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