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Mixture and Alligation


When we mix two or more then 2pure substance , we get what is known as a mixture.
Mixture of Mixtures :- If we mix two mixtures which have components say A and B in the final mixture is given by

RULE oF Mixture
If a contains 'x' liter of liquid 'x' and if 'y' liters is taken out and replaced by 'y' liters of liquid 'z' and if the above step is repeated with the mixture so obtained that is x liter of mixture replaced with y liter of liquid 'z' then if the above operation is repeated 'n' times then

Initial quantity of liquid X contains
Liquid X left in the containes after nth operation
= (
x - y
) n

Initial quantiy of liquid X contains
Amount of Liquid Z the solution container after nth operation
= 1 - (
x - y
) n


In this we find the proportion in which ingredients at given prices must be mixed to produce a mixture at a given price, this is termed as allegation.

RULE of Alligation
If gradients are mixed in a ratio then we can write

Quantity of dearer
Quantity of Cheaper
Mean Price - CP of cheaper
CP of dearer - Mean Price