Alligation or Mixture problems
From container A containing 54 liter of mixture of milk and water in ratio of 8 : 1 , 18 liter of the mixture is taken out and poured into container B in which ratio of milk to water is 3 : 1. If difference between total milk and total water in container B is 30 liter then find the quantity of initial mixture in container B.
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.
By the rule of alligation: Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind Rs. 15 Mean Price Rs. 16.50 Rs. 20 3.50 1.50 ∴ Required rate = 3.50 : 1.50 = 7 : 3.
Here withdrawal of liquid A and B result into making the container empty. Hence percentage of two liquids withdrawn are two components of the percentage by which the container becomes empty. Applying the rule of alligation, we getA : B = 10 : 20 or 1 : 2 Quantity of liquid = 1 (1 + 2) × 90 = 30 liters Quantity of liquid B = 90 ? 30 = 60 liters.
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.
EXAMIANS