Tuesday, 2 June 2026

Bank Exam Practice Material Series Page 14 | Advanced Mixture & Alligation Tricks and Ratio Mixing Methods

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Mixture & Alligation

Ratio Mixing Concepts

Heavy Standard Questions

Speed Tricks

Page 14 – Advanced Mixture & Alligation Tricks and Ratio Mixing Methods

Master advanced mixture and alligation concepts, ratio mixing methods, replacement techniques, and shortcut solving approaches for competitive examinations.

Why Mixture & Alligation is Important

Frequently asked in Bank and SSC exams
Strengthens ratio and percentage concepts
Useful in commercial arithmetic problems
Improves logical calculation ability
Enhances shortcut-solving techniques

Core Concepts Covered

Alligation Rule
Replacement Methods
Weighted Mixing
Price-Based Mixtures
Ratio Distribution Logic

Important Mixture & Alligation Formulas

Alligation Rule

Weighted Average Formula

Replacement Formula

Remaining Quantity = Initial Quantity × (1 − Removed Fraction)ⁿ

Advanced Mixture & Alligation Tricks

Trick 1 – Basic Alligation

Rice costing ₹40/kg mixed with rice costing ₹60/kg. Mean price = ₹50/kg

Ratio:

(60 − 50) : (50 − 40)

10 : 10

Answer = 1 : 1

Trick 2 – Weighted Average Mixing

10 litres milk at ₹40/litre and 20 litres milk at ₹50/litre

Average Price:

(10×40 + 20×50) ÷ 30

1400 ÷ 30

Answer = ₹46.67/litre

Trick 3 – Replacement Method

A container has 100 litres milk. 20 litres removed and replaced with water.

Milk remaining:

100 × (80/100)

Answer = 80 Litres

Heavy Standard Practice Questions

Question 1

Tea worth ₹80/kg mixed with tea worth ₹120/kg to get mixture worth ₹100/kg. Find ratio.

Answer = 1 : 1

Question 2

15 litres solution at ₹30/litre mixed with 25 litres solution at ₹50/litre. Find average price.

Answer = ₹42.5/litre

Question 3

A container contains 80 litres milk. 20 litres removed and replaced with water. Find milk remaining.

Answer = 60 Litres

Question 4

Find ratio of water and milk if 25% mixture is water.

Answer = 1 : 3

Fast Revision Table

Concept	Shortcut Idea
Alligation	Cross subtraction method
Weighted Mixing	Use weighted average directly
Replacement	Apply remaining fraction formula
Mixture Ratio	Convert percentages into ratios