Alligation or Mixture problems
A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?
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.
By the rule of alligation, we have: Profit on 1st part Profit on 2nd part 8% Mean Profit 14% 18% 4 6 Ration of 1st and 2nd parts = 4 : 6 = 2 : 3 ∴ Quantity of 2nd kind = ❨ 3 x 1000 ❩kg = 600 kg.
Total quantity of iron = 4 (1 / 4) + 6 (2 / 3) = 1 + 4 = 5 kg. Total quantity of tin = (4 + 6) ? 5 = 5 kg. In the resultant mixture, iron : tin = 5 : 5 or 1 : 1