Alligation or Mixture problems
Find the quantity of rice @ Rs. 10 per kg. which should be mixed with 25 kgs of rice @ Rs. 8 per kg, so that on selling the mixture @ Rs. 15 per kg there is 80% profit.
Cost price of the mixture = 15 × (100 / 180) = Rs. 25/3 per kg
(Quantity of rice @ Rs. 8 per kg) / (Quantity of rice @ Rs.10 per kg) = (5 / 3) / (1/3) = 1/5
Quantity of rice @ Rs. 10 per kg = 25 × (1/ 5) = 5 kgs.
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.
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.
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