Alligation or Mixture problems
If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain?
Let us assume that the lotion has 50% alcohol and 50% water.ratio = 1:1As the total solution is 9mlalcohol = water = 4.5mlNow if we want the quantity of alcohol = 30%The quantity of water = 70%The new ratio = 3:7Let x ml of water be addedWe get, 4 . 5 4 . 5 + x = 3 7 => x=6Hence 6ml of water is added.
Let he mixes the oils in the ratio = x : y Then, the cost price of the oils = 60x + 65y Given selling price = Rs. 68.20 => Selling price = 68.20(x+y) Given profit = 10% = SP - CP => 10/100 (60x + 65y) = 68.20(x+y)-(60x + 65y) => 6x + 6.5y = 8.20x + 3.20y =>2.2x = 3.3y => x : y = 3 : 2
Let C.P. of 1 liter milk be Re. 1, Gain = 16 2/3 % = 50/3 %and S.P. of 1 liter mixture = Re. 1 then C.P. of 1 liter mixture = (1 x (100 x 3) / 350) = Re. (6 / 7) By the rule of alligation,Hence, required ratio = (1/ 7) : (6 / 7) = 1 : 6