Alligation or Mixture problems
In a 100 litre of mixture the ratio of milk and water is 6:4. How much milk must be added to the mixture in order to make the ratio 3 : 1?
Let the amount of juice and water in original mixture '4x' litre and '3x' litre respectively. According to given data, 4x/3x+6 =8/7 28x=24x+48 28x?24x=48 4x = 48 x = 12 Amount of juice = 4x = 4×12 = 48 litre.
Average speed = (100 / 10) = 10 km/hr. Ratio of time taken at 7 km/hr to 12 km/hr = 2 : 3 Time taken at 7 km/hr = 2 (2 + 3) × 10 = 4 hrs. Distance covered at 7 km/hr = 7 × 4 = 28 km. Distance covered at 12 km/hr = 100 ? 28 = 72 km.
Here, quantity of wine left after third operation = [1 - (5 / 25)]3 x 25 = (4 / 5)3 x 25 = (64 / 125) x 25 = (64 / 5) = 12 4/5 liters. Final ratio of wine to water = (64 / 125) / (1- 64 /125) = (64 / 125) /(61 / 125) Wine : Water = (64 / 61)
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.