Alligation or Mixture problems
Ratio of water and milk in a container is 2 : 3. If 40 liter mixture removed from the container and same quantity of milk is added to it then the ratio of water to milk becomes 1 : 4. Find the initial quantity of mixture?
From the given data, let the initial quantity of the mixture = 5x Then, 2 x - 16 3 x - 24 + 40 = 1 4 8 x - 64 = 3 x + 16 5 x = 80 x = 16 lit Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.
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.
Profit (%) = 9.09 % = 1/11 Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml
Number of liters of water in 150 liters of the mixture = 20% of 150 = 20/100 x 150 = 30 liters.P liters of water added to the mixture to make water 25% of the new mixture.Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).(30 + P) = 25/100 x (150 + P)120 + 4P = 150 + P => P = 10 liters.
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