Allegations and Mixture Formulas

Formula For Mixture and Allegation

Formula For Allegation And Mixtures

Alligation is a way to find the ratio in which two or more ingredients at the given price are mixed to produce a mixture of desired price. This technique can be applied to any topic like mixtures, profit & loss, simple interest, time & distance, percentage, etc.

Formulas to Solve Allegations and Mixtures question :-

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



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 dearerMean 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.

formulas to solve allegation and mixture

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 =x1 — yn units.