Allegation

Mixture:

Mixing of two or more than two type of quantities gives us a mixure.
 

Allegation rule helps us :

  • To find in what ratio two mixtures with different concentrations are to be mixed to get a target concentration.
  • To find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.

Mean Price:

The cost price of a unit quantity of the mixture is called the mean price.

1. Rule of Alligation:

 
If two ingredients are mixed, then
 
(Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c).
 

2. Suppose a container contains x of liquid from which y units are taken out and replaced by water.

 
After n operations, the quantity of pure liquid =
 

Questions Asked from this Chapter:

 

Question Type 1: Based on mixture of only Two ingredients

Example:
Two vessels A and B contains milk and water in the ratio of 4:3 and 2:3. The ratio in which these mixtures be mixed to form a new mixture containing half milk and half water:
a) 7:5
b) 6:5
c) 5:6
d) 4:3
Solution:

Question Type 2: Based on Alloy

Example:
In an alloy there is 12% of copper. To get the 60 Kg of copper, how much alloy will be required?
a) 424 kg
b) 575 Kg
c) 828 Kg
d) 1736*(2/3) Kg
Solution:

Question Type 3: Based on Percent of Ingredients

Example:
A mixture of 40 litres of Milk and water contains 10% of water. How much water must be added to make water 20% in the new mixture?
a) 10 litre
b) 7 litre
c) 5 litre
d) 3 litre
Solution:

Question Type 4: Based on Ratio of Mixture of only two ingredients

Example:
The water and milk in a mixture are in ratio 7:5. When 15 litres of water is added to it, the ratio of milk and water in the new mixture becomes 7:8. The total quantity of water in the new mixture is:
a) 35 litres
b) 40 litres
c) 60 litres
d) 96 litres
Solution:
 

Question Type 5: Based on Ratio of Mixture of Mixture of More than two Ingredients

Example:
An alloy conatins copper, zinc and nickel in the ratio of 5:3:2. The quantity of Nickel in Kg that must be added to 100 Kg of this alloy to have the new ratio 5:3:3 is
a) 8
b) 10  
c) 12
d) 15
Solution:
 

Question Type 6: Based on Profit and Loss

Example:

The ratio of quantities of sugar, in which sugar costing Rs 20 per Kg and Rs 15 per Kg, should be mixed so that there will be neither loss nor gain on selling the mixed sugar at the rate of Rs 16 per Kg is:

a) 2:1

b) 1:2
c) 4:1
d) 1:4
Solution: