Total number of men, women and children working in a company are 27. They earn Rs.18000 in a day. If the sum of the wages of all men, women and children is in ratio of 18: 10: 12 and the wages of an individual man, woman and child is in ratio 6: 5: 3, then find a man's earning in a day.

Let m, w, c be counts and M, W, C be individual wages. m+w+c=27. Total wages ratio 18:10:12 means 18x+10x+12x=18000, so 40x=18000, x=450. Individual wages ratio 6:5:3 means wages are 6y:5y:3y. So m(6y)=18x=8100, w(5y)=10x=4500, c(3y)=12x=5400. From m(6y)=8100 and c(3y)=5400: c(3y)/m(6y)=5400/8100=2/3, so c/m=4/3. Using m+w+c=27 and c=4m/3, we get 13m/3 + w = 27. From w(5y)=4500, w=900/y. Substituting and solving gives y=5, so M=6y=Rs.900.