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TIPS FOR SOLVING QUESTIONS RELATED TO MIXTURE AND ALLIGATION:

1. Mixture: Aggregate of two or more than two type of quantities gives us a mixture.

2. Alligation: It is a method of solving arithmetic problems related to mixtures of ingredients. This rule enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.

3. Alligation Rule: When two elements are mixed to make a mixture and one of the elements is cheaper and other one is costlier then,
\begin{aligned} \frac {Quantity of Cheaper}{Quantity of Costlier} = \frac {C.P. of Costlier - Mean Price}{Mean Price - C.P. of Cheaper} \end{aligned} Thus, (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c).

4. Let a container contains x units of liquid from which y units are taken out and replaced by water.
The quantity of pure liquid after 'n' operations is equal to \begin{aligned}
= \left[ x \left( 1 - \frac{y}{x} \right)^n \right] \\
\end{aligned}