Alligation or Mixture problems
A vessel contains mixture of liquids A and B in the ratio 3: 2. When 20 litres of the mixture is taken out and replaced by 20 litres of liquid B, the ratio changes to 1: 4. How many litres of liquid A was there initially present in the vessel?
21.% of liquid B initially present in the vessel = 2 / (3 + 2) × 100 = 40% % of liquid B finally present in the vessel = 4 / (1 + 4) × 100 = 80% The second solution is liquid B which is being mixed and it has 100% liquid B. 80% of liquid B present in the resultant mixture may be taken as average percentage. So, using rule of alligation on liquid B per cent, we can write, or 1 : 2 The ratio of liquid left in the vessel to liquid B being mixed = 1: 2 Since the quantity of liquid B being mixed is 20 liters, the quantity of liquid left in the vessel is 10 liters. Therefore, the total quantity of liquid initially present in the vessel = 10 + 20 = 30 liters Quantity of liquid A = 3 / (2 + 3) × 30 = 18 liters.