Mixture And Alligation

1. Alligation:
It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.
A process or rule for the solution of problems concerning the compounding or mixing of ingredients differing in price or quality.

2. Mean Price:
The cost price of a unit quantity of the mixture is called the mean price.

3. Basic Formula:
If two ingredients A and B of price x and y respectively are mixed and the price of resultant mixture is M (mean price)then the ratio (R) in which ingredients are mixed is given by,the rule of allegation

R = M?y / x?M

4. Replacement Of Part Of Solution Formula:
Suppose a container contains a solution from which some quantity of solution is taken out and replaced with one of the ingredients. This process is repeated n times then, We can use this formula:
If a container contains a solution from which some quantity of solution is taken out and replaced with one of the ingredients. This process is repeated n times then,

Final Amount of ingredient that is not replaced = Initial Amount (Vol .after removal / Vol .after replacing))ⁿ

5. Mixture Of More Than Two Elements:
These questions may seem a little tricky at first, but it is similar concept applied repeatedly.

In order to calculate final ratio of ingredients when mixture contains more than two ingredients,

1. Take two ingredients such that 1st ingredient is LOWER than the mean value and the other one is HIGHER than the mean value.
2. Calculate the ratio of ingredients
3. Repeat for all possible pairs
4. Final ratio is the ratio obtained from step 2 (if an ingredient is common in the ratios, add values for this particular ingredient)