# Alligation methods – Pharmaceutics – I B. Pharma 1st Semester

Alligation methods

Objective

At the end of this lecture, student will be able to:

• Calculate the amount of diluent required to make a desired lower strength

• Calculate the amounts of active ingredient which must be added to make a higher strength

• Calculate amount of higher and lower strength preparations that must be combined to make a desired amount of an intermediate strength

## Alligation Methods

Alligation is a mathematical technique used in pharmacy and medicine to calculate the quantities of different strength solutions or substances needed to create a desired strength solution. There are three common scenarios in which alligation methods are applied:

1. Calculating the Amount of Diluent Required to Make a Desired Lower Strength:

This scenario is often encountered when a pharmacist or medical professional needs to prepare a solution with a lower concentration of the active ingredient. The formula for this is:

`Quantity of High Strength Solution : Quantity of Diluent = (C2 - C) : (C - C1)`
• C2: The concentration of the higher strength solution.
• C1: The concentration of the desired lower strength solution.
• C: The concentration of the diluent (usually expressed as 0).

Here, you’ll need to solve for the quantity of diluent needed to dilute the higher strength solution to the desired lower strength.

2. Calculating the Amounts of Active Ingredient Which Must Be Added to Make a Higher Strength:

In this scenario, you need to calculate how much of a higher strength solution should be mixed with the lower strength solution to achieve a desired higher strength. The formula is:

`Quantity of Low Strength Solution : Quantity of High Strength Solution = (C2 - C) : (C - C1)`
• C2: The concentration of the higher strength solution.
• C1: The concentration of the lower strength solution.
• C: The concentration of the desired higher strength solution.

This formula helps you determine the quantity of the lower strength solution and the higher strength solution that must be mixed to reach the desired higher strength.

3. Calculating the Amount of Higher and Lower Strength Preparations That Must Be Combined to Make a Desired Amount of an Intermediate Strength:

This scenario involves finding the quantities of both higher and lower strength solutions that need to be mixed to create a solution with an intermediate strength. The formula for this is:

```Quantity of Low Strength Solution : Quantity of High Strength Solution = (C2 - C) : (C - C1) ```
• C2: The concentration of the higher strength solution.
• C1: The concentration of the lower strength solution.
• C: The concentration of the desired intermediate strength solution.

By solving this equation, you can determine how much of each strength solution to combine to achieve the desired intermediate strength.

These alligation methods are valuable tools in compounding and preparing medications, ensuring accurate and precise concentrations of active ingredients to meet specific medical needs. It’s important to carefully calculate and measure these quantities to ensure the safety and efficacy of the final solution.

## Alligation methods

Product with strength A + Product with strength C = Product with intermediate strength B

• The amount of diluent that must be added to a given amount of higher strength preparation to make a desired lower strength.

• The amounts of active ingredient which must be added to a given amount of lower strength preparation to make a higher strength.

• The amount of higher and lower strength preparations that must be combined to make a desired amount of an intermediate strength.

Example

• What is the percentage of alcohol in a mixture of 3000 ml of 40% alcohol, 1000 ml of 60% alcohol and 1000 ml of 70 % alcohol?

% strength  X  quantity  =  Product

40 X 3000  =  120000

60 X 1000  =   60000

70 X 1000  =  70000

Total  5000     250000

Strength of the solution = 250000 / 5000  = 50% V/V

Practice problems

• What is the percentage of zinc oxide in an ointment prepared by mixing 200 g of 10% ointment, 50 g 0f 20% ointment and 100g of 5% ointment?

• What is the % v/v of alcohl in a cough mixture  containing 500 ml of terpin hydrate elixir, 100 ml of chloroform spirit and hydroiodic acid to make up 1000 ml?

Terpin hydrate elixir contains 40% alcohol

Chloroform spirit contains 40% alcohol

Alligation alternate

• ? + ? = Product of strength X

Example

In what proportion should 95% alcohhol be mixed with 30% alcohol to make 70% alcohol?

95  ———–> 70 – 30 = 40

70

30 ————> 95 – 70 = 25

40 parts of 95% alcohol should be mixed with 25 parts of 30% alcohol to get 65 parts of 70% alcohol

Practice problems

• In what proportion should 30% and 15% hydrogen peroxide me mixed to prepare a 3% hydrogen peroxide solution?

• How many ml of 0.9%w/v NaCl solution be prepared from 250 ml of 25%w/v solution?

• How many ml of 50% solution should be mixed with 2175 ml of 10% solution to make a 20%w/v solution?

• How many ml of 50%w/v dextrose and 5%w/v dextrose are required to prepare 5.5 litres of a 10% w/v dextrose solution?

Summary

• Application of alligation method of calculation

• Alligation medial – To obtain the strength of preparation obtained by mixing two different strength preparations

• Alligation alternate – to calculate the quantities of two preparations required to be mixed to obtain a final strength

• Solving problems involving alligation methods

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