Two equations
Always works for exact amounts.
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GMAT Quant
Alligation
Use concentration differences to get a fast mixing ratio when one low and one high concentration create a target.
When to use
Alligation is a ratio shortcut, not a different conservation law.
It compresses the two-equation mixture setup when one low concentration and one high concentration are mixed to reach a target.
Sanity check
The target must lie between the two source concentrations.
If the target is outside the range, a simple mixture of only those two sources cannot produce it.
Difference rule
- Low : High
- (High - Target) : (Target - Low)
- Use
- Percent values as numbers
- Output
- A ratio, not liters yet
Example: mix 15% and 45% to get 25%.
- High - target
- 45 - 25 = 20
- Target - low
- 25 - 15 = 10
- Low : High
- 20 : 10 = 2 : 1
Ratio to amount
Convert ratio parts into actual amounts only if needed.
If the total is 18 L and the ratio is 2:1, there are 3 total parts, so each part is 6 L.
Continue the example.
- Low solution
- 2*6 = 12 L
- High solution
- 1*6 = 6 L
- Check
- 25% is closer to 15%, so more low solution makes sense
Choose the method based on what the question asks.
Alligation
Fast when you need a low:high ratio from two source concentrations.
Mini application
Try this: mix 10% and 70% to get 40%.
What is the low:high ratio?
Solution
The ratio is 1:1.
70 - 40 = 30 and 40 - 10 = 30, so equal amounts produce the midpoint concentration.
Remember this
Cross the concentration gaps into a ratio.
Low : High = distance from target to high : distance from low to target.