In an organization, the total number of employees working in various Departments viz. IT, Marketing, Purchase, HR, Accounts and Production are 4,500. The information regarding department wise percentage of employees was collected and also record about gender ratio of employees was prepared. 18 percent of total number of employees work in IT department and ratio of males to females in IT department is 2 : 1. In Marketing, ratio of males to females is 2 : 3 and number of employees engaged in marketing is 20% of the total employment. 12% of the total numbers of workers are running the HR department and the ratio of males to females in this department is 5 : 1. The fraction of male to females in production department is 3 : 2 and total number of persons employed in this department is 15% of the total workforce. The number of persons occupied in purchase and accounts department is 24% and 11% respectively of the total number of workers. Gender Ratio (Ratio of males to females) in Purchase department is 1 : 1 and in Accounts is 1 : 2.

What is the ratio of total number of males to total number of females working in all the departments put together?

The correct option is 41 : 34.

To find the overall ratio of total males to total females working in all departments put together, let us first calculate the number of males and females in each department.

Total number of employees in the organization = 4,500.

1. IT Department:

Percentage of employees = 18%

Total employees in IT = 18% of 4,500 = 810

Ratio of Males to Females = 2 : 1

Number of Males = (2 / 3) × 810 = 540

Number of Females = (1 / 3) × 810 = 270

2. Marketing Department:

Percentage of employees = 20%

Total employees in Marketing = 20% of 4,500 = 900

Ratio of Males to Females = 2 : 3

Number of Males = (2 / 5) × 900 = 360

Number of Females = (3 / 5) × 900 = 540

3. HR Department:

Percentage of employees = 12%

Total employees in HR = 12% of 4,500 = 540

Ratio of Males to Females = 5 : 1

Number of Males = (5 / 6) × 540 = 450

Number of Females = (1 / 6) × 540 = 90

4. Production Department:

Percentage of employees = 15%

Total employees in Production = 15% of 4,500 = 675

Ratio of Males to Females = 3 : 2

Number of Males = (3 / 5) × 675 = 405

Number of Females = (2 / 5) × 675 = 270

5. Purchase Department:

Percentage of employees = 24%

Total employees in Purchase = 24% of 4,500 = 1,080

Ratio of Males to Females = 1 : 1

Number of Males = (1 / 2) × 1,080 = 540

Number of Females = (1 / 2) × 1,080 = 540

6. Accounts Department:

Percentage of employees = 11%

Total employees in Accounts = 11% of 4,500 = 495

Ratio of Males to Females = 1 : 2

Number of Males = (1 / 3) × 495 = 165

Number of Females = (2 / 3) × 495 = 330

Total Males across all departments:

Total Males = 540 + 360 + 450 + 405 + 540 + 165 = 2,460

Total Females across all departments:

Total Females = 270 + 540 + 90 + 270 + 540 + 330 = 2,040

Ratio of Total Males to Total Females:

$\text{Ratio}=\frac{2460}{2040}=\frac{41}{34}$

Thus, the required ratio of total males to total females working in all departments put together is 41 : 34.