Ramesh has three varieities of rice costing 18 Rs/kg,25 Rs/kg and 36 Rs/kg, In what ratio he should mix these three varieties so that on selling whole mixture at 23.10 Rs/kg he may get a profit of 10?

Selling price is 23.10 Rs/kg with 10% profit, so cost price of mixture = 23.10/1.1 = 21 Rs/kg. Using allegation method: first mix 18 and 36 to get average (18+36)/2 = 27. Then mix 27 with 25 in ratio to get 21. allegation: (27-21):(21-25) = 6:4 = 3:2. So 18:36 ratio is 1:1 (equal quantities). Taking 3 parts each of 18 and 36 gives average 27, then 9 parts of 27 with 6 parts of 25 in 3:2 ratio. Therefore final ratio = 9:3:2 for costs 18, 25, 36 respectively.