## Alligation Rule

When two elements are mixed to make a mixture and one of the elements is cheaper and other one is costlier then,

Here Mean Price is CP of mixture per unit quantity.

Above rule can be written as,

Then,

Cheaper Quantity : Costlier Quantity = (D – M) : (M – C)

## Shortcut Formulas for Mixture and Alligation

**Rule 1**

If n different vessels of equal size are filled with the mixture of P and Q in the ratio p_{1} : q_{1}, p_{2} : q_{2}, ……, p_{n} : q_{n} and content of all these vessels are mixed in one large vessel, then

**Rule 2**

If n different vessels of sizes x_{1}, x_{2}, …, x_{n} are filled with the mixture of P and Q in the ratio p_{1} : q_{1}, p_{2} : q_{2}, ……, p_{n} : q_{n} and content of all these vessels are mixed in one large vessel, then

**Rule 3: Removal and Replacement**

If a vessel contains “x” litres of liquid A and if “y” litres be withdrawn and replaced by liquid B, then if “y” litres of the mixture be withdrawn and replaced by liquid B, and the operation is repeated ‘n’ times in all, then :

**Rule 4:**

p gram of ingredient solution has a% ingredient in it. To increase the ingredient content to b% in the solution