Mixtures & Alligation for CAT: Concepts & PYQs

Mixture questions are frequent enough to matter and combine cleanly with ratios, averages and percentages. For CAT preparation, the useful question is not “Have I finished the chapter?” but can I recognise the version of the concept CAT hides inside a word problem and choose an efficient method under time pressure?

What to know

The core checklist for this topic is: Weighted concentration, alligation, replacement, repeated replacement, price mixtures, purity/concentration. Learn these as connected ideas rather than isolated formulas. CAT often combines two of them in one question.

Recurring CAT-style forms

Expect questions built around Mix two concentrations, remove-and-replace, repeated dilution, target average price, adding pure ingredient/water. The wording changes, but the mathematical structure repeats. Your first 20–30 seconds should be spent identifying that structure before writing equations.

Decision rules worth remembering

• Alligation ratio = (higher−mean):(mean−lower)
• removed mixture has current concentration
• repeated replacement leaves fraction (1−removed/total)^n

One original example

To make 35% solution from 20% and 50%, alligation gives (50−35):(35−20)=15:15=1:1. Equal quantities work here because the target is exactly midway.

The point of a worked example is not the answer; it is the choice of representation. After solving, ask whether a ratio table, base-100 assumption, sign chart, factorisation or diagram made the work shorter.

Common traps

• Removing only one component instead of mixture
• using initial concentration after replacement
• reversing alligation ratio
• confusing quantity ratio with concentration ratio

These traps are valuable because they explain why a student can “know the formula” and still lose marks. Add the exact mistake to your error log when it occurs; do not simply write “silly mistake.”

How to practise

Start with 10–15 untimed questions until the first step becomes automatic. Then use mixed timed sets where this topic is not announced in advance. Finish with sectionals and mock review. Mastery checkpoint: Can decide whether to use weighted average, alligation or algebra within 20–30 seconds.

Once that checkpoint is stable, move on rather than over-polishing one chapter. CAT QA is a portfolio of scoring areas; the objective is enough reliable topics to make question selection easy on exam day.