Question

Suppose the average salary of male employees is 520 Birr and that of females is 420 Birr. The
mean salary of all employees is 500 Birr. Find the ratio of the number of male and female
employees.

Answer 1

Explanation:

Given :-

The average salary of male employees is 520 Birr and that of females is 420 Birr.

The mean salary of all employees is 500 Birr.

To find :-

The ratio of the number of male and number of female employees.

Solution :-

Let the number of male employees be X

Let the number of female employees be Y

Given that

The average salary of male employees

= 520 Birr

We know that

Average = Sum of all observations / Number of all observations

Average salary of male employees

= Sum of the salaries of all male employees / Number of male employees

=> 520 = Sum of the salaries of all male employees / X

=> Sum of the salaries of all male employees = 520×X

= 520X Birr

And

Given that

The average salary of female employees

= 420 Birr

We know that

Average = Sum of all observations / Number of all observations

Average salary of female employees

= Sum of the salaries of all female employees / Number of female employees

=> 420 = Sum of the salaries of all female employees / Y

=> Sum of the salaries of all female employees = 420×Y

= 420Y Birr

Number of all male and female employees = X+Y

The sum of the salaries of all male and female employees = ( 520X+420Y ) Birr

We know that

Average = Sum of all observations / Number of all observations

Given that

The mean salary of all employees

= 500 Birr

Therefore,

500 = (520X+420Y)/(X+Y)

=> 500(X+Y) = 520X+420Y

=> 500X+500Y = 520X+420Y

=> 520X+420Y = 500X+500Y

=> 520X-500X = 500Y-420Y

=> 20X = 80Y

=> X/Y = 80/20

=> X/Y = 4/1

=> X : Y = 4:1

=> No.of male : No. female = 4:1

Therefore, Required ratio = 4:1

Answer :-

The ratio of the number of male and number of female employees = 4:1

Used formulae:-

→ Average = Sum of all observations / Number of all observations

→ a:b can be written as a/b