Module 1 · Arithmetic
Chapter 5: Mixtures & Alligations
Arithmetic
4 topics
What this chapter covers
The 4 topics below make up Mixtures & Alligations on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Weighted average & alligation
| Weighted average (mean of blend) | M = (q₁c₁ + q₂c₂) / (q₁ + q₂) |
|---|---|
| Alligation rule (ratio of quantities) | q₁ : q₂ = (c₂ − M) : (M − c₁) |
| Cheaper : dearer (price mix) | (Dearer − Mean) : (Mean − Cheaper) |
| Mean lies between the two | c₁ < M < c₂ always |
| Two-mixtures combine | treat each mixture’s concentration as one ingredient |
Dilution & repeated replacement
| Concentration after adding water | new % = pure / (total + added) × 100 |
|---|---|
| Repeated replacement (final pure) | final = initial × (1 − x/V)ⁿ |
| Replacement as a ratio | final : initial = (V − x)ⁿ : Vⁿ |
| Equal successive draws of x from V | fraction left = (1 − x/V)ⁿ |
| Water added after n replacements | V − final pure quantity |
CAT reference
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