CAT Mixtures & Alligations Study Notes

Mixtures and Alligations for CAT

This chapter deals with mixing two or more ingredients with different qualities (price, concentration, profit, etc.) to form a mixture. It's a core Arithmetic concept tested directly and in Data Interpretation sets. Mastery of the alligation rule is crucial for speed.

1. Basic Concepts and Definitions

2. The Alligation Rule

The rule is visually represented by the alligation cross/chequeboard.

[IMAGE: Alligation Cross Diagram showing C1, C2, M, and differences (C2-M) and (M-C1)]

Alligation for more than two components

Apply alligation sequentially. First, mix two to get an intermediate mean, then mix that mean with the third ingredient, and so on.

3. Applications Beyond Simple Price

A. Profit & Loss on Mixtures

If a mixture is sold at a price, the cost price of the mixture becomes the 'mean price' for alligation.

B. Replacement of Mixture

When part of a mixture is removed and replaced with a pure ingredient, use the formula for successive replacement.

C. Average Weight/Height/Age

Alligation can be used for any weighted average situation.

4. Advanced Scenarios & Shortcuts

Alligation with Three Variables

When three ingredients are mixed and two constraints are given (e.g., final price and proportion of one ingredient), set up equations.

Mixture of Mixtures

Find the effective price/concentration of each mixture first, then treat them as ingredients for the final alligation.

Successive Mixing / Stepwise Alligation

A key time-saver. When a mixture is added to another, find the concentration/price after each step.

[VIDEO: "CAT Successive Replacement Mixtures Shortcut"]

5. Quick Strategy for CAT

Time Allocation: A direct alligation question should take 45-60 seconds. A moderate mixture DI caselet should take 2-3 minutes.

Mental Math Shortcut: For two-ingredient alligation, the ratio differences are simply the differences from the mean. Visualize the cross instantly.

Common Trap Avoidance:

Ensure the 'Mean Price' is a weighted average, not a simple average.
In replacement problems, the total volume often remains constant. Use the (1 - x/M)^n formula for speed.
When alligating percentages, ensure you are alligating the right component (e.g., alcohol% vs water%).

Practice Approach: Start with basic two-item price alligation. Move to three-item and profit-based mixtures. Then tackle replacement problems. Finally, integrate with arithmetic and DI practice.