Mixture & Alligation

Alligation Rule

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

Mixture and Alligation shortcut methods

Here Mean Price is CP of mixture per unit quantity.
Above rule can be written as,

Mixture and Alligation Shortcut Formulas

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 p1 : q1, p2 : q2, ……, pn : qn and content of all these vessels are mixed in one large vessel, then

Mixture and Alligation shortcuts

 

Rule 2
If n different vessels of sizes x1, x2, …, xn are filled with the mixture of P and Q in the ratio p1 : q1, p2 : q2, ……, pn : qn and content of all these vessels are mixed in one large vessel, then

Mixture and Alligation Shortcut Methods

 

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If a vessel contains “x” litres of liquid A and if “y” litres be withdrawn and replaced by liquid B, then if “y” litres of the mixture be withdrawn and replaced by liquid B, and the operation  is repeated ‘n’ times in all, then :

Mixture and Alligation Shortcut Methods

 

Rule 4:
p gram of ingredient solution has a% ingredient in it. To increase the ingredient content to b% in the solution

Mixture and Alligation Shortcut Formulas