Correct Answer - Option 1 : 50 years
Given:
The number of employees = 200
The average age of 200 employees = 58 years
The number of male employees = 3/5 part of total employees
The ratio of the average age of male employees to female employees = 5 : 7
Formula used:
Average = (the sum of observations/the total number of observations)
The sum of observations = average × the total number of observations
Calculation:
Let the average age of male employees and the average age of female employees be (5x) years and (7x) years respectively
The number of male employees = (3/5) × 200
⇒ 3 × 40
⇒ 120
And the number of female employees = total number of employees - the number of male employees
⇒ 200 - 120
⇒ 80
The total age of 200 employees = 200 × 58
⇒ 11600 years
The total age of 120 males = 5x × 120
⇒ (600x) years
The total age of 80 females = 7x × 80
⇒ (560x) years
The total age of 200 employees = The total age of 120 male employees + The total age of 80 female employees
⇒ 11600 = 600x + 560x
⇒ 1160x = 11600
⇒ x = 11600/1160
⇒ x = 10
The average age of male employees = 5x
⇒ 5 × 10
⇒ 50 years.
∴ The average age of male employees is 50 years.
