Ratio and Proportion

Concept:Weighted average or alligation method to find the ratio of two groups when the overall mean and group means are known.Explanation:Let the percentage of males be $x\%$ and females be $(100-x)\%$.The overall mean salary is given by the weighted average:$\frac{27000x + 17000(100-x)}{100} = 25000$.Multiply both sides by 100:$27000x + 17000(100-x) = 2500000$.Simplify:$27000x + 1700000 - 17000x = 2500000$.$10000x + 1700000 = 2500000$.Subtract $1700000$:$10000x = 800000$.Divide by $10000$:$x = 80$.Thus males are $80\%$ and females are $20\%$.Answer:Males: $80\%$, Females: $20\%$.