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Mixtures and Alligation

Mixtures and Alligation​

Weighted average:

Mean = (q1*v1 + q2*v2) / (q1 + q2)

Alligation:

Cheaper quantity : Dearer quantity
= (Dearer value - Mean) : (Mean - Cheaper value)

Use alligation when:

  • Mixing two concentrations.
  • Mixing two prices.
  • Combining two speeds for same type of quantity.
  • Combining two groups with known averages.

Replacement formula:

Final amount of original liquid
= initial amount * (1 - removed volume / total volume)^n

Concentration shortcut:

Pure solute = concentration * total quantity

Common traps:

  • Alligation gives quantity ratio, not value ratio.
  • In replacement, the container is refilled to the same total volume each time.