Alligation involves mixing preparations of different strengths to produce an intermediate strength. It is calculated by: 1) Subtracting the required percentage from the stronger percentage. 2) Subtracting the weaker percentage from the required percentage. 3) The differences are the proportions of the stronger and weaker preparations to mix. For example, to make 100g of an 8% substance by mixing 10% and 2% preparations, the calculation is: 1) Subtract 8% from 10% = 2% 2) Subtract 2% from 8% = 6% 3) Mix 6 parts of 10% and 2 parts of 2% preparations. This gives 75g

1. ALLIGATION
Involves the mixing of two similar preparations, but of different strengths, to produce
preparation of intermediate strength.
Example 1
100 grams of a powder containing 8 per cent of substance x are to be made from
powder containing 10 per cent of x and powder containing 2 per cent of x.
Let n be the number of grains of the 10 per cent powder required. Then 100 - n grams will be
the weight of 2 per cent powder required.
Therefore,
10 2 8
× ������ + × 100 – ������ = × 100
100 100 100
10������ + 200 − 2������ = 800
8������ = 600
������ = 75
i.e. 75 grams of the 10 per cent powder will be mixed with 25 grams of the 2 per cent powder.
Allegation method
The quantities are set out as follows;-
10 2
00
00
00 8
6 2
Subtract 8 from 10 = 2 (required percentage from stronger percentage)
Subtract 2 from 8 = 6 (weaker percentage from required percentage) (Continue overleaf)
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2. Then 6 part of the 10 percent powder plus 2 parts of the 2 per cent powder will produce
8 part of 8 percent powder. 100 grams are required.
Therefore, quantity of 10 per cent powder required
100
= × 6 = 75������
8
And quantity of 2 per cent powder required
100
= × 2 = 25������
8
Example 2
Prepare 1000 grams of Dilute Acetic Acid from Acetic Acid.
Acetic Acid B.P. = 33% w/w
Dilute Acetic Acid B.P. = 6% w/w
Let n be the number of grams of 33 per cent acid required. Then
33 6
× ������ = × 1000
100 100
6000
33������ = 6000 ������������������ ������ = = 182������
33
It should be obvious that this may be written down in the first instance as;
6
× 1000 = 182������.
33
Check by allegation;
33 0
0000
00
6
6 27
7
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3. i.e. subtract 0 (for water ) from 6 = 6
Subtract 6 from 33 = 27
Then 6 part by weight of Acetic Acid 33 per cent plus 27 parts by weight of water will give 33
part by weight of Dilute Acetic Acid 6 per cent. 1000 gram required,
Therefore, the quantity of 33 % acid required
1000
= ×6
33
= 182
And the quantity of water required
1000
= × 27 = 818 ������
33
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