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Ratio & Proportion for CAT: Formulas, Weightage & Question Types

Think in parts: chain ratios, transfers that change a ratio, and whole-number answers.

Ratio & Proportion formula sheet

Everything CAT needs from Ratio & Proportion, 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

A ratio a:ba:bmeans the quantities are akak and bkbk for some kk
In lowest termskk is the size of one "part"
a:b=c:da:b = c:d  ⟺  ad=bc\iff ad = bc
Componendo–dividendoab=cd  ⟹  a+ba−b=c+dc−d\dfrac{a}{b} = \dfrac{c}{d} \implies \dfrac{a+b}{a-b} = \dfrac{c+d}{c-d}

Chaining two ratios

Given a:ba:b and b:cb:cscale both so the shared term matches
Formallya:b:c=a1c1:b1c1:b2c2a:b:c = a_1c_1 : b_1c_1 : b_2c_2 after matching on bb
Three or morechain one link at a time, always through the shared term

Proportion

Directy=kxy = kx — doubling one doubles the other
Inversey=kxy = \dfrac{k}{x} — doubling one halves the other
To a powery∝x2y \propto x^2 means y=kx2y = kx^2
Combinedy∝xzwy \propto \dfrac{xz}{w} means y=kxzwy = \dfrac{kxz}{w}

What changes a ratio, and what does not

Multiplying both parts by mmthe ratio is unchanged
Adding the same amount to boththe ratio moves toward 1:11:1
A transfer between the twothe total is unchanged — use it as the anchor
Each part changing by its own %treat as two separate multipliers

Sub-groups and overall ratios

Group ratio and sub-ratios givenassign separate letters to each sub-group, then force the group ratio
Interest, output or costif two ratios multiply (e.g. amount ×\times rate), the result ratio is the product term by term
Removing one group's sharesubtract its amounts from the totals, then re-form the ratio

Integer conditions

a:ba:b in lowest termsthe real values are akak and bkbk with kk a positive integer
A totalmust be a multiple of the sum of the parts
A bound on the totalgives a bound on kk, and the extreme answer comes from the extreme kk

The 6 Ratio & Proportion 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

    A transfer, or a sale, changes the ratio

  2. 02

    Chain two ratios through a shared term

  3. 03

    Sub-group ratios inside a whole

  4. 04

    The same amount added to each part

  5. 05

    Whole numbers force the answer

  6. 06

    Proportional to something

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Ratio & Proportion in CAT: quick answers

How many Ratio & Proportion questions come in CAT Quant?
About 0.7 questions in a 22-question Quant section, worth roughly 2 marks. Ratio & Proportion appeared in 17 of the 24 CAT papers from 2017 to 2025, 21 questions in all, which ranks it 19 of 25 Quant chapters.
Are Ratio & Proportion questions in CAT MCQ or TITA?
29% of the Ratio & Proportion questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Ratio & Proportion questions does CAT ask?
CAT keeps returning to 6 question shapes in Ratio & Proportion: A transfer, or a sale, changes the ratio; Chain two ratios through a shared term; Sub-group ratios inside a whole; The same amount added to each part; Whole numbers force the answer; Proportional to something.

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