The following pie chart shows the percentage distribution of a total of 1600 employees in different departments of a
company. The table shows the ratio of male to female employees in different departments. Study the information and answer
the question that follows.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746991802/aptidude_questions/xwavidkr8g5ase1hvhgf.png)

What is the percentage of the number of employees in production department to the number of female employees of all the
departments taken together? (correct to one decimal place)

Question

The following pie chart shows the percentage distribution of a total of 1600 employees in different departments of a
company. The table shows the ratio of male to female employees in different departments. Study the information and answer
the question that follows.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746991802/aptidude_questions/xwavidkr8g5ase1hvhgf.png)

What is the percentage of the number of employees in production department to the number of female employees of all the
departments taken together? (correct to one decimal place)

Accepted Answer

#### **Step 1: Find the number of employees in the Production department**
- Total employees = 1600
- Production department = 30% of 1600  
  $$ = \frac{30}{100} 	imes 1600 = 480 $$

#### **Step 2: Find the number of female employees in each department**

| Department  | % of Employees | M : F Ratio | Female Employees |
|-------------|----------------|-------------|------------------|
| HR          | 8%             | 3 : 5       | $$ \frac{5}{8} 	imes 128 = 80 $$ |
| IT          | 15%            | 2 : 3       | $$ \frac{3}{5} 	imes 240 = 144 $$ |
| Accounts    | 25%            | 3 : 7       | $$ \frac{7}{10} 	imes 400 = 280 $$ |
| Marketing   | 22%            | 7 : 4       | $$ \frac{4}{11} 	imes 352 = 128 $$ |
| Production  | 30%            | 5 : 3       | $$ \frac{3}{8} 	imes 480 = 180 $$ |

**Calculations:**
- HR: $$ \frac{5}{8} 	imes (8\% 	imes 1600) = \frac{5}{8} 	imes 128 = 80 $$
- IT: $$ \frac{3}{5} 	imes (15\% 	imes 1600) = \frac{3}{5} 	imes 240 = 144 $$
- Accounts: $$ \frac{7}{10} 	imes (25\% 	imes 1600) = \frac{7}{10} 	imes 400 = 280 $$
- Marketing: $$ \frac{4}{11} 	imes (22\% 	imes 1600) = \frac{4}{11} 	imes 352 = 128 $$
- Production: $$ \frac{3}{8} 	imes (30\% 	imes 1600) = \frac{3}{8} 	imes 480 = 180 $$

#### **Step 3: Total number of female employees**
$$ 80 + 144 + 280 + 128 + 180 = 812 $$

#### **Step 4: Calculate the required percentage**
$$
	ext{Required Percentage} = \left(\frac{480}{812}ight) 	imes 100 \approx 59.1\%
$$

### Correct Answer:
**59.1%**

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