Alligation or Mixture problems
A merchant has 50 kg. of sugar part of which he sells at 8 % profit and the rest at 18 % profit. He gains 14 % on the whole. The quantity sold at 18 % profit is ?
Quantity of milk @ Rs.10 per liter / Quantity of milk @ Rs. 16 per liter = 1 / 2 So, quantity of milk @ Rs. 10 per liter = 26 / 2 = 13 liter.2nd Method Let us assume shopkeeper buy P liter milk of price @ Rs. 10 per liter.Buy price of 26 liter of milk @ Rs. 16 per liter = 26 x 16Buy price of P liter of milk @ Rs. 10 per liter = P x 10Sell price of total milk ( P + 26 ) @ Rs. 14 per liter = 14 x ( P + 26 ) According to question there is no loss or no profit.Then Buy Price = Sell Price 26 x 16 + P x 10 = 14 x ( P + 26 ) ? 26 x 16 + 10P = 14P + 14 x 26 ? 26 x 16 - 26 x 14 = 14P - 10P? 2 x 26 = 4P? 4P = 2 x 26? P = 2 x 26 / 4 = 13So, quantity of milk @ Rs. 10 per liter = 13 liter.
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 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
Ratio of milk andwater = 4:1 Quantity of water = 35/5 = 7 litres Quantity of milk = 35 X 4/5 = 28 litres If 7 litre of water is added, new quantity of water = 14 litre New ratio of milk and water = 28:14 = 2:1