⚗️ Alligation & Mixture - Formula Sheet

🎯 Core Formula

Alligation Rule

     (Cheaper Quantity)         (Dearer Quantity)
            |                        |
   Mean Price - Cheaper Price    Dearer Price - Mean Price
            |                        |
            --------------------------
                      |
                      Ratio

Formula:

(Cheaper Quantity) : (Dearer Quantity) = (Dearer Price - Mean Price) : (Mean Price - Cheaper Price)

📊 Weighted Average

Weighted Average = (Sum of Weighted Values) / (Sum of Weights)

🔢 Mixture Problems

Replacement Formula

Final Quantity = Initial Quantity × (1 - x/n)^t

Where:

• x = quantity replaced each time
• n = total quantity
• t = number of replacements

Repeated Dilution

Final Concentration = Initial Concentration × (1 - removal/total)^n

⚡ Quick Tips

1. Alligation Diagram: Draw the alligation cross for visual clarity
2. Mean Price: Always between cheaper and dearer prices
3. Ratio: Simplify the ratio to lowest terms
4. Units: Keep all quantities in same units

📝 Practice Formulas

Alloy Problems

Quantity of Metal A = Total Quantity × (Percentage of A) / 100

Solution Mixing

Concentration = (Amount of Solute / Total Solution) × 100

Master Alligation - Draw the cross, find the ratio! ⚗️