# Allegations and Mixture Formulas

## Formulas to Solve Allegations and Mixtures ques:-

#### What is an Allegation?

When two ingredients X and Y of price p and q respectively are mixed together, such that the price of the resultant mixture is M (mean price), then the ratio (R) in which ingredients are mixed is given by, the rule of the allegation:

(Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c)

#### What is a Mixture?

In a mixture two or more ingredients are mixed together to get a desired quantity. The quantity can be expressed as ratio or percentage.

For example: When two varieties of sugar are mixed to form a new variety of sugar then it is called as a mixture.

#### What is a Mean Price?

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

## Formulas to Solve Mixture and Allegations

### Formula 1 for Allegations and Mixtures

When two commodities are mixed then , Quantity of cheaper = C.P. of dearer(d) – Mean Price(m) Quantity of dearer Mean price(m) – C.P. of cheaper(c)

### Formula 2 Allegations and Mixtures

Consider a container contain x unit of liquid A from which y units are taken out and replaced by water. This operation is repeated n number of times, then the quantity of pure liquid will be given by the formula:

Quantity =  [x (1-y/x)^n] units. Therefore, (Cheaper Commodity) : (Dearer Commodity) = (d – m) : (m-c)

### Formula 3 Mixtures and Allegations

Calculate quantity of pure Liquid after ‘n’ successive operations:

If a container contains ‘x’ units of pure liquid , and we replace the liquid with ‘y’  units of water :

Then after ‘n’ successive operations, the units of pure liquid left is :

 After n operations, the quantity of pure liquid = x 1 – y n units. x 