Alligation or Mixture problems
In what ratio must a mixture of 20% milk strength be mixed with that of 60% milk strength so as to get a new mixture of 25% milk strength?
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.
Here total parts of milk and water in the solution is 6+2 = 8 parts. 1part = 640/8 = 80 old mixture contains 6parts of milk and 2 parts of water(6:2). To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same. i.e, 4 x 80 = 320 ml.
Let the quantity of the wine in the cask originally be x litres Then, quantity of wine left in cask after 4 operations = x 1 - 8 x 4 litres ? x 1 - 8 x 4 x = 16 81 ? 1 - 8 x 4 = 2 3 4 ? x = 24
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