CAT Averages Mixtures and Alligation Formula Sheet PDF Download 2026

Averages, Mixtures and Alligation Weightage in CAT: Previous Year Questions Analysis

As per CAT Averages, Mixtures and Alligation weightage from past years, students can expect 6-7 questions from this topic every year, with 2021 as the highest-yielding year at 12 questions. This figure combines three closely related tags in the tagged past-paper data (Averages, Mixture Problems, and Mixtures and Alligations), since CAT does not release an official chapter-wise weightage of its own.

This is one of the heavier Arithmetic topics on the paper, and the count has stayed at 4 or more every single year since 2016. Averages also feeds directly into other topics − a Time, Speed and Distance or Data Interpretation question routinely needs the same weighted-average logic taught here.

Average Formula for CAT: How to Calculate Simple and Weighted Averages

A plain average assumes every value counts equally − the moment quantities differ, it stops being the right tool:

Five scores summing to 325 average to 65. The formula itself is never the hard part; identifying what counts as a "value" is.

Adding or removing one value shifts the average by less than the new value's own gap from it, since the shift gets diluted across every value, not just the new one:

When quantities differ, a weighted average replaces the plain one:

2 kg of a Rs.100/kg item mixed with 3 kg of a Rs.150/kg item averages to Rs.130/kg, not the plain average of Rs.125 − the heavier quantity pulls the average toward itself.

CAT 2022 (Slot 1). The average of three integers is 13, so their sum is 39. Include a natural number n so the new average of four integers stays an odd integer: (39+n)/4 must be odd, and the smallest such n is 5, giving a new average of 11.

Average Speed Formula for CAT: Why 2xy/(x+y) Not (x+y)/2

Covering the same distance once at speed x and once at speed y never averages to (x+y)/2 − that formula only applies when the time at each speed is equal, not the distance:

40 km/h one way and 60 km/h back averages to 2 × 40 × 60 / 100 = 48 km/h, not 50 − more time is spent at the slower speed, so it pulls the average down toward itself. Confusing distance-equal with time-equal is the single most common error in this section.

Alligation Rule for CAT: How to Mix Two Quantities to a Target Strength

The alligation rule finds the ratio in which two strengths must be mixed to hit a target strength, without ever needing the actual quantities:

Mixing a 16%-coffee blend with a 36%-coffee blend to hit 24% needs a ratio of (36−24):(24−16) = 12:8 = 3:2 by weight − only the three strengths matter, not the actual amounts.

CAT 2019 (Slot 1). A chemist mixes two liquids: one litre of liquid 1 weighs 1 kg, one litre of liquid 2 weighs 800 gm, and half a litre of the mixture weighs 480 gm. For volume fraction x of liquid 1, 0.5(0.8 + 0.2x) = 0.48 gives x = 0.8, so liquid 1 is 80% of the mixture by volume − the same alligation logic run on densities instead of prices.

Repeated Replacement Formula in Mixtures: How to Solve Removal and Replacement Problems

When a fraction of a mixture is removed and replaced with a pure substance, repeating the process n times compounds the loss:

A 40-litre mixture that is 10% acid has 4 litres of acid. Removing and replacing 10 litres with water twice leaves 4 × (1−10/40)² = 4 × 0.5625 = 2.25 litres of acid. The exponent counts repetitions, not litres removed − a single removal-and-replacement is this same formula with n=1.

Mixing Two Mixtures Formula for CAT Quantitative Aptitude

When two ready-made mixtures with different ratios are combined, each one's own ratio has to be weighted by the volume actually taken from it:

10 litres of a 3:2 milk-water mix combined with 15 litres of a 2:3 milk-water mix gives milk = 10 × 3/5 + 15 × 2/5 = 6 + 6 = 12 litres of milk in 25 litres total, a 12:13 ratio.

Averages and Mixtures Questions for CAT with Solutions PDF

Averages, Mixtures and Alligation questions in CAT rarely test one formula in isolation. Below are two real CAT questions with solutions:

Q1 (CAT 2022, Slot 1). The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

(a) 3   (b) 4   (c) 5   (d) 1

Q2 (CAT 2019, Slot 1). A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then the percentage of liquid 1 in the mixture, in terms of volume, is

(a) 80   (b) 70   (c) 85   (d) 75

Neither question is answered by a single formula on this sheet on its own − both need the base setup chained with another relation, which is the real skill this sheet is meant to build.

Averages, Mixtures and Alligation Concept Video for CAT with Solved Examples

Source: MBA Wallah

How to Revise Averages, Mixtures and Alligation Before CAT

The closing page repeats every formula in one table, each checked against real numbers.

• Cover the formula column and reproduce it from the quantity name
• Ask whether every item is weighted equally before reaching for a plain average
• Re-derive the alligation ratio from the cross method rather than memorising the final expression alone
• Check whether a speed question holds distance or time equal before picking a formula