Quantitative Aptitude :: Alligation or Mixture

A mixture contains two or more ingredients of certain quantity mixed together to get the desired quantity. The quantity can be expressed as ratios or percentage. When two varieties of rice are mixed to form a new variety of rice then it is called as a mixture.

If two ingredients A and B of price x and y respectively are mixed and 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.

The cost of a unit quantity of the mixture is called the mean price.

If two ingredients are mixed, then

\(\left(\frac{Quantity \ of \ cheaper}{Quantity \ of \ dearer}\right)\) = \(\left(\frac{C.P. \ of \ dearer \ - \ Mean \ Price}{Mean \ price \ - \ C.P. \ of \ cheaper}\right)\)

We present as under:

Suppose a container contains x of liquid from which y units are taken out and replaced by water.

After n operations, the quantity of pure liquid = \(\left[ x \left( 1 - \frac{y}{x}\right)^{n}\right]\) units.