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 number of males in marketing department to the number of males in Hr department?

The correct option is 4 : 5.

Let's calculate the number of male employees in both the Marketing and HR departments step-by-step.

Step 1: Total workforce in the organization

Total number of employees = 4,500

Step 2: Calculate the number of males in the Marketing Department

The number of employees in the Marketing department is 20% of the total workforce.

Total employees in Marketing = 20% of 4,500

$=\frac{20}{100}\times 4500=900$

The ratio of males to females in the Marketing department is given as 2 : 3.

Therefore, the fraction of male employees in Marketing = $\frac{2}{2+3}=\frac{2}{5}$

Number of males in Marketing = $\frac{2}{5}\times 900=360$

Step 3: Calculate the number of males in the HR Department

The number of employees in the HR department is 12% of the total workforce.

Total employees in HR = 12% of 4,500

$=\frac{12}{100}\times 4500=540$

The ratio of males to females in the HR department is given as 5 : 1.

Therefore, the fraction of male employees in HR = $\frac{5}{5+1}=\frac{5}{6}$

Number of males in HR = $\frac{5}{6}\times 540=450$

Step 4: Find the required ratio

Ratio of number of males in Marketing to the number of males in HR = 360 : 450

Dividing both terms by 90:

$\text{Required Ratio}=\frac{360}{450}=\frac{4}{5}$

Hence, the ratio of the number of males in the Marketing department to the number of males in the HR department is 4 : 5.