# 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

Pharmaceutical calculations

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