Quant Notes | Mixture allegation

Example 1: In what ratio must a shopkeeper mix two types of rice worth Rs. 50 kg and Rs. 70 kg, so that the average cost of the mixture is Rs. 65 kg?

Q1. How much of salt at 42 paise/kg must be mixed with 25kg of salt at 24 paise/kg, so that a profit of 25% is obtained by selling the mixture at 40 paise /kg?

Q2. A merchant has 840kg of rice, part of which he sells at 9% profit and the rest at 16% profit. He must gain 12% profit on the whole. What is the quantity sold at 16% profit?

Alligation Method 2- Repeated Dilution
This is used to calculate pure quantity left after 'n' number of processes of repeated replacement is done on the pure quantity. Suppose, a container contains 'x' units of a liquid from which 'y' units are taken out and replaced by water. After 'n' operations quantity of pure-

Q1. A Container contains 192 liter of Milk. A seller draws out x% of Milk and replaced it with the same quantity of water. He repeated the same process for 3 times. And thus Milk content in the mixture is only 81 liter. Then how much percent he withdraw every time?
1. 10%
2. 15%
3. 18%
4. 20%
5. 25%
Solution- 
81 = 192(1-x/100)³
x = 25%

Q2.  A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y respectively. When 10 liter of the mixture is taken out and replaced it water, then the ratio becomes 2:3. Then what is the initial quantity of Milk in the Jar?
1. 12 Liter
2. 15 Liter
3. 18 Liter
4. 20 Liter
5. None
Solution- 
x+y =30
(x-10*x/x+y)/ (y-10*y/(x+y) + 10) = 2/3
2x-4/3y = 20
x =18

Q3. A Jar contains 100 liters of Milk a thief stole 10 liter of Milk and replaced it with water. Next, he stole 20 liter of Milk and replaced it with water. Again he stole 25 liter of Milk and replaced with water. Then what is the quantity of water in the final mixture?
1. 55 Liter
2. 54 Liter
3. 50 Liter
4. 46 Liter
5. None
Solution-
Milk = 100*90/100*80/100*75/100 = 54
Water = 100-54 = 46