Aptitude
Alligations and Mixture
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A mixture, as the name suggests is mixing two or more things together and alligation enables us to find the ratio in which the ingredients/ things have been mixed to form the mixutre.
The Alligation and Mixture Formulas can be applied to any topic like mixtures, profit and loss, simple interest, time and distance, percentage, etc.
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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.
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The rule of alligation
$(Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c)$
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In a mixture, two or more ingredients are mixed together to get a desired quantity. The quantity can be expressed as ratio or percentage.
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Example : When two varieties of sugar are mixed to form a new variety of sugar then it is called as a mixture.
The cost of a unit quantity of the mixture is called the mean price.
Alligation and Mixture Formulas 1
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When two commodities are mixed then ,
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Then the average speed will be :
$\frac{\text{Qantity of Cheaper}}{\text{Quantity of Dearer}} = \frac{\text{C.P of Dearer(d) - Mean Price(m)}}{\text{Mean Price(m) – C.P. of Cheaper(c)}}$
When their is replacement of one with another commodity
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Consider a container contain x unit of liquid A from which y units are taken out and replaced by water.
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This operation is repeated n number of times, then the quantity of pure liquid will be given by the formula:
Quantity= $[x–(1–( \frac{x}{y} )^n) ]units$
Alligation and Mixture Formulas 3
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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 ,
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This operation is repeated n number of times, then the quantity of pure liquid will be given by the formula:
Quantity = $x (1 - \frac{y}{x})n $ units.