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Mixtures & Alligation for CAT: Formulas, Weightage & Question Types

Alligation, repeated remove-and-replace, and liquid moved between vessels.

Mixtures & Alligation formula sheet

Everything CAT needs from Mixtures & Alligation, 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 one rule

Always trackthe amount of each component, never the percentage
Amountfraction×total volume\text{fraction} \times \text{total volume}
Whypercentages shift when the total changes; amounts only change when you add or remove

Alligation — mixing two things of known strength

Quantities xx at strength pp, yy at strength qq, result rrxy=q−rr−p\dfrac{x}{y} = \dfrac{q-r}{r-p}
In wordsthe distances from the mean are in the reverse ratio of the quantities
It works forconcentration, price per kg, density, or any other "per unit" quantity
It does not work foranything that is not per-unit — totals, or quantities themselves

Successive replacement — remove some, top up, repeat

Remove fraction ff each time, nn timesremaining original == start ×(1−f)n\times (1-f)^n
Removing volume vv from total VVremaining original == start ×(1−vV)n\times \left(1-\dfrac{v}{V}\right)^n
The total volumenever changes
Ratio after nn rounds(1−f)n:1−(1−f)n(1-f)^n : 1-(1-f)^n

Transfers between two vessels

Take vv from A to B, stir, take vv backthe amount of A's liquid now in B equals the amount of B's liquid now in A
Whyboth vessels end with the volume they began with, so whatever left must have been replaced

Mixing by weight and by volume

Volumes in ratio a:ba:b, densities in ratio c:dc:dweights are in ratio ac:bdac : bd
Strength p%p\%pp grams in every 100 ml

With cost and profit

Cost of the mixture per unitthe weighted average of the component costs
Selling pricecost×(1+profit %)\text{cost} \times (1 + \text{profit }\%)
Part sold at a different pricework in totals — total revenue needed minus revenue already taken

The 6 Mixtures & Alligation 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

    Alligation, once

  2. 02

    Three or more components

  3. 03

    Remove and replace, repeatedly

  4. 04

    Liquid moved between vessels

  5. 05

    A mixture with a price on it

  6. 06

    Dilute to hit a target ratio

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Mixtures & Alligation in CAT: quick answers

How many Mixtures & Alligation questions come in CAT Quant?
About 1.1 questions in a 22-question Quant section, worth roughly 3 marks. Mixtures & Alligation appeared in 22 of the 24 CAT papers from 2017 to 2025, 29 questions in all, which ranks it 9 of 25 Quant chapters.
Are Mixtures & Alligation questions in CAT MCQ or TITA?
21% of the Mixtures & Alligation questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Mixtures & Alligation questions does CAT ask?
CAT keeps returning to 6 question shapes in Mixtures & Alligation: Alligation, once; Three or more components; Remove and replace, repeatedly; Liquid moved between vessels; A mixture with a price on it; Dilute to hit a target ratio.

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