CAT Percentages Formula Sheet PDF Download 2026

Percentages Weightage in CAT: Previous Year Questions Analysis

As per CAT Percentages weightage from past years, students can expect 3-4 questions from this topic every year, with 2019 as the highest-yielding year at 7 questions. CAT does not release an official chapter-wise weightage, so the numbers below are based on tagging every question from the released papers by topic and year.

The count has swung more than Profit and Loss's over the same stretch − a single question in 2022, seven in 2019 − so treat the average as a guide, not a guarantee. Percentages also underpins other topics directly: a Profit and Loss or Time and Work question routinely needs the same base and successive-change formulas taught on this sheet, so the real exposure to this topic is higher than the standalone count above.

Percentage Formula for CAT: The Basic Definition and Swap Rule

Every percentage question comes down to the same first move: read the percentage as a multiplier, not as a separate step of arithmetic.

20% of 80 is not "find 20, then find 80, then combine" − it is one multiplication, 0.2 × 80 = 16.

A less obvious formula saves time on awkward numbers − x% of y always equals y% of x:

4% of 75 is awkward to compute directly. 75% of 4 = 3 is the same answer and faster to reach.

Percentage Shortcut Tricks for CAT Quantitative Aptitude

Memorising the fraction-to-percentage table converts awkward decimals into quick mental multiplication, and it is one of the highest-return shortcuts for this topic:

37.5% of 216 done directly means multiplying by 0.375, which invites a slip. Converting 37.5% to 3/8 first and working out 216 × 3/8 = 81 in one line is both faster and safer.

Successive Percentage Change Formula: How to Calculate Two Changes Together

When a value changes twice in a row, the two percentage changes never simply add:

Up 20% then down 20% gives 20 − 20 − 400/100 = −4%, a net loss rather than a wash, because the rise sits on the smaller number and the fall on the larger one.

CAT 2024 (Slot 3). After two successive salary increments, Gopal's pay became 187.5% of what it started at, and the second increment's percentage was exactly double the first's. Setting up (1+x/100)(1+2x/100) = 1.875 and solving gives x = 25% for the first increment − the same net-of-two-changes formula above, run backwards to find one of the two rates instead of the combined result.

A related formula covers two quantities held at a fixed product, such as price and quantity purchased:

Price up 25% (= 1/4) means consumption has to fall 1/5 = 20% to keep total spending unchanged − price × quantity, speed × time, and men × days all follow this identical rule.

Percentage Comparison Formula in CAT: A More Than B vs B Less Than A

"A is x% more than B" and "B is x% less than A" are not mirror statements − they use different bases, and CAT wording exploits exactly that gap:

A is 25% more than B makes B only 20% less than A, not 25% less, because the first statement's base is B and the second's is A.

Percentage Points vs Percentage Change: What's the Difference

A rate moving from one percentage to another can be described two different ways, and CAT questions are written to make the reader pick the wrong one:

5% to 7% is 2 percentage points, but it is a 40% rise in the rate itself − both numbers are correct, but they answer different questions.

Percentages Questions for CAT with Solutions PDF

Percentages questions in CAT rarely test the base definition alone and usually combine it with another relation from this sheet. Below are two real CAT questions with solutions:

Q1 (CAT 2021, Slot 3). In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be

(a) 80   (b) 78   (c) 84   (d) 86

Q2 (CAT 2020, Slot 1). In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

(a) 62   (b) 55   (c) 59   (d) 66

Neither question is answered by a single formula on this sheet on its own − both need the base-100 setup chained with another relation, which is the real skill this sheet is meant to build.

Percentage Concept Video for CAT with Solved Examples

Source: MBA Wallah

How to Revise Percentages Before CAT

The closing page repeats every formula in one table, each checked against a base of 100.

• Cover the formula column and reproduce it from the quantity name
• Say the base out loud before starting any calculation − percent of what?
• Re-derive the net-of-two-changes formula rather than memorising the final expression alone
• Check whether a question wants a percentage point difference or a percentage change whenever a rate moves