Alligation or Mixture problems
The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
Milk in 1-litre mixture of A = 4/7 litre. Milk in 1-litre mixture of B = 2/5 litre. Milk in 1-litre mixture of C = 1/2 litre. By rule of alligation we have required ratio X:Y X : Y 4/7 2/5 \ / (Mean ratio) (1/2) / \ (1/2 ? 2/5) : (4/7 ? 1/2) 1/10 1/1 4 So Required ratio = X : Y = 1/10 : 1/14 = 7:5
Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have : Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice ? (20-x)/(x-15) = 2/3 ? 60 - 3x = 2x - 30 ? x = 18.
Let initially milk and water in container B is 3x liter and x liter respectively
Now, 3x + (8/9) × 18 ? x ? (1/9) × 18 = 30
3x + 16 ? x ? 2 = 30
x = 8
Initial quantity is container B = 8 (3 + 1) = 32 Liter.
EXAMIANS