Guide
Percentages are a foundation for profit/loss, SI-CI, DI, growth rates, ratios and many arithmetic word problems even when a question is not labelled 'percentage'. 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: Percentage as fraction/ratio, percentage change, successive change, reverse percentage, percentage points vs percent, population/growth; and expenditure-income, base-value choice. 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 Successive increase/decrease, restoring original value after change, comparing two quantities as % more/less, changing numerator and denominator, income-expenditure-savings, and DI growth rates. 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
- x% of y = y% of x
- successive change a+b+ab/100
- reverse change uses new base
- if A is x% more than B, B is x/(100+x)% less than A
One original example
If A is 40% more than B, set B=100 and A=140. Then B is 40/140 = 28.57% less than A. This is why 'x% more' and 'x% less' are not symmetric.
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
- 20% up and 20% down is not zero
- confusing percentage point with percentage change
- using wrong denominator when saying 'more than/less than'
- assuming equal absolute change gives equal percentage change
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 solve reverse-percentage and successive-change questions without writing lengthy 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.
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