Bank Exam Speed Maths
Page 13: Mixture & Alligation (Shortcut Methods)
1. Basic Concept
Mixture: Combination of two or more items
Alligation: Method to find ratio of mixing
Used for prices, percentages, concentrations
2. Alligation Rule
Ratio = (Difference of mean with higher value) : (Difference with lower value)
Example:
Mix ₹20/kg and ₹30/kg to get ₹25/kg
Ratio = (30-25) : (25-20) = 5 : 5 = 1 : 1
Mix ₹20/kg and ₹30/kg to get ₹25/kg
Ratio = (30-25) : (25-20) = 5 : 5 = 1 : 1
3. Weighted Average Concept
Mean = (Sum of (Value × Quantity)) / Total Quantity
Example:
10 items at ₹20 and 20 items at ₹30
Mean = (200 + 600) / 30 = ₹26.67
10 items at ₹20 and 20 items at ₹30
Mean = (200 + 600) / 30 = ₹26.67
4. Replacement Concept
When part of mixture is replaced:
Remaining quantity = (1 - removed/total)n
Example:
10 litres, remove 2 litres once
Remaining = 8/10 = 4/5
10 litres, remove 2 litres once
Remaining = 8/10 = 4/5
5. Important Shortcut
If mean is closer to one value, quantity of that value is higher
Example:
Mean = 28 (between 20 & 30)
Closer to 30 → more quantity of 30
Mean = 28 (between 20 & 30)
Closer to 30 → more quantity of 30
6. Important Tips
• Use alligation instead of long calculations
• Focus on ratio, not actual values
• Common in DI and profit-loss questions
7. Practice Questions
1. Mix ₹40 and ₹60 to get ₹50 → Ratio?
2. Mean of 10 items at ₹20 and 10 at ₹40?
3. Replace 2 litres from 10 litres → Remaining fraction?
4. Mix 30% and 50% to get 40% → Ratio?
5. Which has more quantity if mean closer to higher value?
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