Alligation or Mixture problems
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
By the rule of alligation, we have: Strength of first jar Strength of 2nd jar 40% MeanStrength 26% 19% 7 14 So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2 ∴ Required quantity replaced = 2 3
Ratio of milk and water = 2 : 1Quantity of milk = 60 X 2/3 = 40 litreQuantity of water = 20 litreTo make ratio, 1: 2, we have to double the water that of milkSo, water should be 80 litre.That means 80 ? 20 = 60 litre water to be added.
Let us assume the number of boys = B and number of girls = G.According to question,B + G = 30Lets us assume total weight of boys = W1 and total weight of girls = W2average weight of boys = total weight of boys/number of boystotal weight of boys/number of boys = 20W1/B = 20W1 = 20Baverage weight of girls = total weight of girls/number of girls25 = W2/GW2 = 25GData is not sufficient to solve the equation.since we do not know either the average weight of the whole class or the ratio of no. of boys to girls.
According to figure we find that the ratio will be 3 : 1.Quantity sold at 20% profit = 3 / (3 + 1) × 50 = 37.5 kgs. Quantity sold at 40% profit = (50 ? 37.5) = 12.5 kgs.
By the rule of alligation: C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.
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