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.|