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Percentages for CAT: Formulas, Weightage & Question Types

Multiply, don't add, and always ask "per cent of what?"

Percentages formula sheet

Everything CAT needs from Percentages, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place.

The basics

x%x\% of yyxy100\dfrac{xy}{100}
Percentage changenew−oldold×100\dfrac{\text{new}-\text{old}}{\text{old}} \times 100
Increase by x%x\%multiply by (1+x100)\left(1+\dfrac{x}{100}\right)
Decrease by x%x\%multiply by (1−x100)\left(1-\dfrac{x}{100}\right)

Multipliers — the tool that does the work

+20%+20\%×1.2\times 1.2
−20%-20\%×0.8\times 0.8
Successive changesthe multipliers multiply, they never add
Up x%x\% then down x%x\%×(1−x210000)\times\left(1-\dfrac{x^2}{10000}\right) — always a net loss
A is x%x\% more than BB is 100x100+x%\dfrac{100x}{100+x}\% less than A
Price up x%x\%, same spendquantity falls by 100x100+x%\dfrac{100x}{100+x}\%

Fractions worth knowing on sight

12,13,14,15\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}50%50\%, 3313%33\frac{1}{3}\%, 25%25\%, 20%20\%
16,17,18,19\frac{1}{6}, \frac{1}{7}, \frac{1}{8}, \frac{1}{9}1623%16\frac{2}{3}\%, 1427%14\frac{2}{7}\%, 12.5%12.5\%, 1119%11\frac{1}{9}\%
111,112,116\frac{1}{11}, \frac{1}{12}, \frac{1}{16}9111%9\frac{1}{11}\%, 813%8\frac{1}{3}\%, 6.25%6.25\%

Relations between quantities

A is x%x\% of BA=Bx100A = \dfrac{Bx}{100}
Per capitatotalpopulation\dfrac{\text{total}}{\text{population}}
So the population multiplier istotal multiplierper-capita multiplier\dfrac{\text{total multiplier}}{\text{per-capita multiplier}}
Two groups combinedthe overall percentage is a weighted average — alligation applies

Chained shares

"a%a\%, then b%b\% of the rest"what survives is (1−a100)(1−b100)\left(1-\dfrac{a}{100}\right)\left(1-\dfrac{b}{100}\right)
Each stage's baseis the remainder, not the original total

The 6 Percentages question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

  1. 01

    One change after another

  2. 02

    Two groups, one overall figure

  3. 03

    An integer has to come out whole

  4. 04

    A chain of relations

  5. 05

    Marks and a pass mark

  6. 06

    A percentage of what is left

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Percentages in CAT: quick answers

How many Percentages questions come in CAT Quant?
About 0.9 questions in a 22-question Quant section, worth roughly 3 marks. Percentages appeared in 19 of the 24 CAT papers from 2017 to 2025, 28 questions in all, which ranks it 11 of 25 Quant chapters.
Are Percentages questions in CAT MCQ or TITA?
29% of the Percentages questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Percentages questions does CAT ask?
CAT keeps returning to 6 question shapes in Percentages: One change after another; Two groups, one overall figure; An integer has to come out whole; A chain of relations; Marks and a pass mark; A percentage of what is left.

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