Bank Exam Speed Maths Master Series Page 14 | Mixture & Alligation Tricks & Fast Calculation Methods

 

 Bank Exam Speed Maths Master Series – Page 14

Mixture & Alligation Tricks & Fast Calculation Methods

Shaktimatha Learning – Speed Maths Academy
Learn Mixture & Alligation shortcut tricks, aptitude formulas, and fast calculation methods for Bank Exams, SSC, Railways, Insurance, and Competitive Exams.

 Importance of Mixture & Alligation in Competitive Exams

Mixture & Alligation is one of the most important arithmetic topics in:

• Bank Exams
• SSC
• Railway Exams
• Insurance Exams
• Quantitative Aptitude

This topic is highly useful in:

• Profit & Loss
• Percentage calculations
• Ratio & Proportion
• Business mathematics
• Data Interpretation

🎯 What is Mixture?

Mixture means combining two or more quantities into a single quantity.

Examples:

• Milk & Water
• Gold mixtures
• Chemical mixtures
• Price mixtures

🎯 What is Alligation?

Alligation is a shortcut method used to compare:

• Mean price
• Mean percentage
• Mean concentration

 Basic Alligation Formula

0

 Trick 1: Basic Alligation Method

Example:

Rice worth ₹40/kg and ₹60/kg mixed to get mixture worth ₹50/kg

Apply alligation:

60 − 50 = 10
50 − 40 = 10

Ratio:

10 : 10

✅ Answer = 1 : 1

 Trick 2: Unequal Difference Method

Example:

Milk worth ₹20/litre and ₹30/litre mixed to get ₹24/litre

Higher difference:

30 − 24 = 6

Lower difference:

24 − 20 = 4

Ratio:

6 : 4

3 : 2

✅ Answer = 3 : 2

Trick 3: Water & Milk Mixture

Example:

Milk : Water = 4 : 1

Total mixture = 25 litres

Total parts = 5

Milk:

25 × 4/5 = 20 litres

Water:

25 × 1/5 = 5 litres

✅ Answer = 20 litres milk, 5 litres water

 Trick 4: Replacement Method

Formula:

1

Where:

• x = quantity removed
• y = total quantity
• n = number of operations

Example:

A vessel contains 100 litres milk.

20 litres removed and replaced twice.

Remaining milk:

100(1−20/100)²

100(0.8)²

100 × 0.64

✅ Answer = 64 litres

Trick 5: Mean Price Shortcut

Example:

10 kg rice at ₹40/kg
20 kg rice at ₹50/kg

Mean price:

(10×40 + 20×50)/30

1400/30

✅ Answer = ₹46.67/kg

Important Observation Trick

In alligation:

• Cross difference method is fastest
• Ratio comes diagonally

 Important Mixture & Alligation Shortcuts

Topic	Shortcut
Alligation	Cross difference
Mean Price	Weighted average
Water-Milk	Ratio parts method
Replacement	Remaining formula
Mixture Ratio	Difference method

 Practice Questions

1. Rice worth ₹30 and ₹50 mixed to get ₹40. Find ratio
2. Milk : Water = 3 : 2, total mixture = 25 litres. Find milk quantity
3. 15 kg rice at ₹40 and 25 kg rice at ₹60. Find mean price
4. A vessel contains 80 litres milk. 20 litres replaced once. Remaining milk = ?
5. Sugar solution 20% and 40% mixed to get 30%. Find ratio

✅ Answers

1. 1 : 1
2. 15 litres
3. ₹52.5/kg
4. 60 litres
5. 1 : 1

🎯 Preparation Strategy:
Practice cross difference methods, weighted averages, replacement formulas, and ratio simplification daily to improve arithmetic speed and quantitative aptitude solving ability.

“Smart Shortcut Methods Make Mixture Problems Simple & Scoring.”

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