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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