. The average monthly salary paid to all employees in a company was Rs 8,000. The average monthly salaries paid to male and female employees of the company were Rs 10,600 and Rs 7,500 respectively. Find out the percentages of males and females employed by the company.
Let the number of male employees be x and the number of female employees be y.
According to the given information:
Average monthly salary paid to all employees = Rs 8,000
So, (Total salary paid to all employees)/(Total number of employees) = 8,000.
Total salary paid to all employees = Average monthly salary paid to all employees * Total number of employees
Total salary paid to all employees = 8,000 * (x + y) ...............(1)
Average monthly salary paid to male employees = Rs 10,600
So, (Total salary paid to male employees)/x = 10,600
Total salary paid to male employees = 10,600x ..............(2)
Average monthly salary paid to female employees = Rs 7,500
So, (Total salary paid to female employees)/y = 7,500
Total salary paid to female employees = 7,500y ..............(3)
According to the given information:
(Total salary paid to male employees) + (Total salary paid to female employees) = Total salary paid to all employees
10,600x + 7,500y = 8,000 * (x + y)
10,600x + 7,500y = 8,000x + 8,000y
2,600x = 500y
26x = 5y ...............(4)
We can rewrite equation (4) as:
y = (26/5)x
Now, to find the percentage of males and females employed by the company, we need to find the ratio of the number of males to the total number of employees and the ratio of the number of females to the total number of employees.
(Percentage of males) = (Number of males) / (Total number of employees) * 100
= x / (x + y) * 100
= x / (x + (26/5)x) * 100 ............from equation (4)
= x / ((5x + 26x)/5) * 100
= 5x / 31x * 100
= (5/31) * 100
= 500/31
(Percentage of females) = (Number of females) / (Total number of employees) * 100
= y / (x + y) * 100
= (26/5)x / ((5x + 26x)/5) * 100
= (26/5) * 5x / 31x * 100
= 26/31 * 100
= 2600/31
Therefore, the percentage of males employed by the company is approximately 16.13% and the percentage of females employed by the company is approximately 83.87%.