Question

The mean annual salary of all employees in a company is Rs. 25,000. The mean salary of male and female employees is Rs. 27,000 and 17,000 respectively. Find the percentage of male and female employed by the company.

Answer 1

Step-by-step explanation:

Use alligation method

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Answer 2

The percentage of male and female employed by the company are 80% and 20% respectively.

Step-by-step explanation:

Let x be the number of men and y be the number of women.

$Mean=\dfrac{\text{Sum of observations}}{\text{Number of observations}}$

$Mean\times \text{Number of observations}=\text{Sum of observations}$

It is given that the mean annual salary of all employees in a company is Rs. 25,000.

Total number of employees = 25000(x+y)

The mean salary of male and female employees is Rs. 27,000 and 17,000 respectively.

Number of men = 27000x

Number of women = 17000y

$25000(x+y)=27000x+17000y$

Divide both sides by 1000.

$25(x+y)=27x+17y$

$25x+25y=27x+17y$

$25x-27x=-25y+17y$

$-2x=-8y$

$\frac{x}{y}=\frac{-8}{-2}$

$\frac{x}{y}=\frac{4}{1}$

The ratio of men to women is 4:1.

Percentage of male = $\frac{4}{4+1}\times 100=80\%$

Percentage of female = $\frac{1}{4+1}\times 100=20\%$

Therefore, the percentage of male and female employed by the company are 80% and 20% respectively.

#Learn more

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