Question

In a company with 600 employees, the average age of the male employees is 42 years and that of the female employees is 41 years. If the average age of all the employees in the company is 41 years 9 months, then the number of female employees is:

• A. 150
• B. 450
• C. 350
• D. 250

Answer 1

Answer:

A. 150

Solution:

Solution:

Given data:       

No. of employees in company = 600

The average age of the male employees = 42 years

The average age of the female employees = 41 years

The average age of all the employees in the company = 41 years 9 months

⇒ $(41 +\frac{9}{12}) years$

⇒ $\frac{167}{4} years$

Concept used:

Average = (Sum of all cases)/(Number of cases)

Calculation:

Let no. of male employees be x.

⇒ No. of female employees = 600 – x.

Sum of ages of all male employees = x × 42

⇒ 42x years      ----(1)

Sum of ages of all male employees = $(600-x)\times{41}$

⇒ (24600 – 41x) years      ----(2)

Sum of ages of all employees = 42x + 24600 – 41x      ----(Adding equation 1 and 2)

⇒ (x + 24600) years      ----(3)

Sum of ages of all employees =$600\times{\frac{167}{4}}$

⇒ 25050 years      ----(4)

Equating equations 3 and 4

⇒ x + 24600 = 25050

⇒ x = 450

⇒ No. of male employees = 450

⇒ No. of female employees = 600 – 450

⇒ 150

∴ The number of female employees in the company is 150.

Alternate method:

No. of male employees: No. of female employees = 3 : 1

⇒ No. of male employees = 3x

⇒ No. of female employees = x

⇒ Total no. of employees = 4x

⇒ 4x = 600      ----(given data)

⇒ x =$\frac{600}{4}$

⇒ x = 150

⇒ No. of female employees = x = 150

 

∴ The number of female employees in company is 150.