Alligation Practice Problems

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Alligation is used to mix two preparations of different strengths to make an intermediate strength. Alligation alternate starts from two known strengths and finds the quantity of each to mix; alligation medial starts from known quantities and finds the resulting strength. The alternate method uses a grid where you take diagonal differences to get the parts of each component.

Formulaparts of high = target − low • parts of low = high − target • volume of each = (its parts ÷ total parts) × final volume

Worked example

Make 250 mL of 25% dextrose from 70% and 10% stock. Parts of 70% = 25 − 10 = 15; parts of 10% = 70 − 25 = 45; total = 60. Volume of 70% = (15 ÷ 60) × 250 = 62.5 mL (and 187.5 mL of the 10%).

💡 Don't confuse the two: medial = known quantities → find strength; alternate = known strengths → find quantities.