Alligation or Mixture problems
Two casks of 48 and 42 liters are filled with mixture of wine and water13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 liters of water added to the whole what will be the proportion of wine to water in the result?
Wine Water 8L 32L 1 : 4 20 % 80% (original ratio) 30 % 70% (required ratio) In ths case, the percentage of water being reduced when the mixture is being replaced with wine. so the ratio of left quantity to the initial quantity is 7:8 Therefore , 7 8 = 1 - K 40 => K = 5 Lit
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 the price of the mixed variety be Rs. x per kg. By rule of alligation, we have: Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice Rs. 15 Mean Price Rs. x Rs. 20 (20 - x) (x - 15) ∴ (20 - x) = 2 (x - 15) 3 ⟹ 60 - 3x = 2x - 30 ⟹ 5x = 90 ⟹ x = 18.
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