Ratio & Proportion for CAT: Concepts & PYQs

Ratios are the language of CAT arithmetic and also simplify mixtures, work, speed, averages and DI. 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: Equivalent ratios, proportion, direct/inverse variation, division in a ratio, partnership, ratio after change; and combining ratios, scale factors. 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 A:B and B:C combine, values added/removed then ratio changes, ages, income-expenditure ratios, efficiency/time inverse ratios, and speed-time-distance ratios. 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

• If work fixed, speed×time constant
• if work same, efficiency×time constant
• combine ratios via common term
• ratio gives relative not absolute values

One original example

If A:B=3:5 and B:C=10:7, scale the first ratio to 6:10. Therefore A:B:C=6:10:7. The shared term must match before ratios can be combined.

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

• Adding ratio terms directly
• forgetting inverse relation
• assuming a ratio fixes actual values
• mixing ratios with percentages without common base

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 convert a word problem into a compact ratio table before forming equations.

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.