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Formulas to Solve Alligations and Mixtures question :- What is an Alligation? 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 alligation. (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 Alligations Alligation and Mixture Formulas 1 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) Alligation and Mixture Formulas 2 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 = \left[x – (1 – \left(\frac{Y}{X}\right)^n \right] units