# Alligation Method in Pharmacy Calculation

Alligation is a rapid arithmetic method used to solve problems related to mixtures of ingredients with different concentrations or strengths to form the desired concentrations or strengths.

#### Application of Alligation Method in Pharmaceutics

• The amount of diluent that must be added to a given amount of higher strength formula to make a desired lower strength.
• The amounts of active ingredient that must be added to a given amount of lower strength formula to make a higher strength.
• The amount of higher and lower strength active ingredient that must be combined to make a desired strength.

There are two types of alligation method:

Alligation medial: Alligation medial is used to find the quantity of a mixture given the quantities of its ingredients. For example, if you have 200 mL of a 5% solution and 400 mL of a 10% solution, what is the concentration of the final mixture?

Alligation alternate: Alligation alternate is used to find the amount of each ingredient needed to make a mixture of a given quantity and concentration or strength. For example, if you want to prepare 1000 mL of a 10% solution using a 5% solution and a 20% solution, how much of each solution do you need?

#### Alligation Formula for Pharmaceutical Calculation

Q1 / Q2 = (Cm - C2) / (C1 – Cm)

Where Q is quantity, C is concentration or strength, 1 and 2 are the ingredients, and m is the mixture.

For example, if you want to prepare 100 mL of a 15% solution using a 10% solution and a 20% solution, you can use this formula to find Q1 and Q2:

Q1 / Q2 = (15 - 10) / (20 - 15);

Q1 / Q2 =5/5

Q1 / Q2 =1

This means that Q1 and Q2 are equal.

We also know that,

Qm = Q1 + Q2

So, Q1 = Qm/2

Q1 =100/2

Q1=50

and,

Q2 = Qm/2

Q2 = 100/2

Q2 = 50

Therefore, you need 50 mL of each solution to make 100 mL of a 15% solution.

Example-1:

Example-2: