Mixture & Alligation Formula
Mixture & Alligation formulas and a topic-wise mock test for quantitative aptitude placement exams like TCS NQT, Infosys, and Wipro. Revise, then practice.
Key Mixture & Alligation Formulas
Mixture Fundamentals - Combining Different Values
Mixture problems involve combining different ingredients to achieve a desired average value. The alligation method provides the exact ratio needed.
- Alligation Rule: (Cheaper - Mean) / (Mean - Dearer) = Quantity of Dearer / Quantity of Cheaper
- Mean Value = (n1×a1 + n2×a2) / (n1 + n2)
- Example: Mix ₹60/kg and ₹80/kg to get ₹70/kg → Ratio=(80-70):(70-60)=1:1
Replacement Problems - Successive Changes
Replacement problems involve removing a portion of a mixture and replacing it with another substance.
- Single Replacement: Final = Initial × (1 - r/100)^n
- Each replacement reduces the original concentration exponentially
- Example: 20% replaced with water → Final = Initial × 0.8
- After 2 replacements: Final = Initial × 0.8² = Initial × 0.64
Advanced Mixture Applications
Practical applications of mixture and alligation concepts.
- Example 1: Mix ₹60 & ₹80 to get ₹70 → (80-70):(70-60)=1:1 → equal quantities
- Example 2: 20% replaced → 80% concentration × 0.8 = 64%
- Example 3: 25% replaced 3 times → Final = Initial × 0.75³ = 42.19%
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