Calculating Regular Female Employee Percentage in a Factory

This problem involves using ratios and percentages to determine the number of male and female employees, the total number of regular employees, and finally, the percentage of regular employees among the female workforce. Let's break down the information given:

• Total number of employees in the factory: 400
• Ratio of male to female employees: 5 ∶ 3
• Total percentage of regular employees in the factory: 87.5%
• Percentage of regular male employees: 92%

We need to find the percentage of regular female employees.

Step 1: Determine the Number of Male and Female Employees

The ratio of male to female employees is 5 ∶ 3. This means for every 5 male employees, there are 3 female employees. The total number of parts in the ratio is $5 + 3 = 8$.

To find the number of male employees, we take the male part of the ratio (5) and divide it by the total parts (8), then multiply by the total number of employees (400):

Number of male employees $= \frac{5}{8} \times 400$

Number of male employees $= 5 \times \frac{400}{8}$

Number of male employees $= 5 \times 50 = 250$

To find the number of female employees, we take the female part of the ratio (3) and divide it by the total parts (8), then multiply by the total number of employees (400):

Number of female employees $= \frac{3}{8} \times 400$

Number of female employees $= 3 \times \frac{400}{8}$

Number of female employees $= 3 \times 50 = 150$

So, there are 250 male employees and 150 female employees. Let's check: $250 + 150 = 400$, which matches the total number of employees.

Step 2: Calculate the Total Number of Regular Employees

We are given that 87.5% of the total employees are regular employees. The total number of employees is 400.

Total number of regular employees $= 87.5\% \text{ of } 400$

To calculate 87.5%, we can convert it to a decimal (0.875) or a fraction ($87.5/100 = 875/1000 = 7/8$). Using the fraction is often easier:

Total number of regular employees $= \frac{7}{8} \times 400$

Total number of regular employees $= 7 \times \frac{400}{8}$

Total number of regular employees $= 7 \times 50 = 350$

So, there are 350 regular employees in the factory.

Step 3: Calculate the Number of Regular Male Employees

We know that 92% of the male employees are regular employees. The number of male employees is 250.

Number of regular male employees $= 92\% \text{ of } 250$

Number of regular male employees $= \frac{92}{100} \times 250$

Number of regular male employees $= 0.92 \times 250 = 230$

So, there are 230 regular male employees.

Step 4: Calculate the Number of Regular Female Employees

The total number of regular employees is 350. This total is made up of regular male employees and regular female employees.

Total regular employees = Regular male employees + Regular female employees

We can find the number of regular female employees by subtracting the number of regular male employees from the total number of regular employees:

Number of regular female employees = Total regular employees - Number of regular male employees

Number of regular female employees $= 350 - 230 = 120$

So, there are 120 regular female employees.

Step 5: Calculate the Percentage of Regular Female Employees

We need to find what percentage of the total female employees are regular employees. The total number of female employees is 150, and the number of regular female employees is 120.

Percentage of regular female employees $= \frac{\text{Number of regular female employees}}{\text{Total number of female employees}} \times 100\%$

Percentage of regular female employees $= \frac{120}{150} \times 100\%$

We can simplify the fraction $\frac{120}{150}$ by dividing both the numerator and denominator by 30:

$\frac{120 \div 30}{150 \div 30} = \frac{4}{5}$

Now, multiply by 100%:

Percentage of regular female employees $= \frac{4}{5} \times 100\%$

Percentage of regular female employees $= 0.8 \times 100\% = 80\%$

Therefore, 80% of the female employees are regular employees.

Summary of Calculation Steps:

• Calculated male employees: 250
• Calculated female employees: 150
• Calculated total regular employees: 350
• Calculated regular male employees: 230
• Calculated regular female employees: 120
• Calculated percentage of regular female employees: 80%

Revision Table: Key Figures

Additional Information on Ratios and Percentages

Ratios and percentages are useful tools for comparing quantities and understanding proportions within a whole. A ratio expresses the relative size of two or more values, while a percentage expresses a quantity as a fraction of 100. In this problem, we used the ratio to divide the total workforce into male and female groups, and then used percentages to find the portions of regular employees within the total group and the male group, ultimately allowing us to isolate and calculate the percentage for the female group.

Understanding how to convert between fractions, decimals, and percentages is crucial for solving such problems. For instance, 87.5% can be thought of as 87.5 out of 100, which simplifies to 7 out of 8 as a fraction. Similarly, 92% is 92 out of 100, or 23 out of 25. Using these conversions can sometimes simplify calculations.