Percentages Formulas for CAT 2026: 18 Shortcuts + 20 PYQs
Percentage formulas for CAT 2026 are the highest-leverage block in the entire Quants section. Arithmetic contributes roughly 35 to 40% of CAT Quant weightage every year, and percentages sits at the top of that arithmetic pyramid because every other topic in the cluster, from Profit and Loss to Mixtures to Simple Interest, is a percentage application in disguise. This cheatsheet pins 18 shortcuts across four recognition blocks, then closes with 20 CAT-level questions that mirror the patterns setters actually use.
The reason most online content on this topic underperforms is that it explains percentages as a fraction-of-a-hundred definition and stops there. CAT 2026 will not test that. CAT 2026 tests successive chains, reverse traps, and percentage application inside multi-step word problems. The 18 shortcuts below are organised around those question types so each formula maps to a recognition cue, not to a textbook chapter order.
Why Percentage Formulas Are the CAT Arithmetic Foundation
Percentages do not show up as one direct question per paper. They show up as a foundation layer beneath roughly half the Quants section. A Profit and Loss question is a markup percentage applied to cost price. A Simple Interest question is a percentage rate compounded over time. A Mixtures and Alligation question is a weighted average of percentage concentrations. A Data Interpretation set is six to eight percentage calculations packed inside one graph. Master the percentages cheatsheet and the entire Arithmetic cluster compresses.
This is the gap most CAT preparation content misses. Aspirants treat the topic as a beginner chapter, finish it in one sitting, and move on to what they perceive as harder material. The pattern: their Profit Loss and SI CI scores never compound because the percentage layer underneath was never automated. The fix is to drill the 18 shortcuts until each one fires within two seconds of seeing a question. The recognition reflex is what compounds, not the formulas themselves.
The 18 Percentage Formulas for CAT 2026
The cheatsheet groups all 18 shortcuts into four blocks. Each block has a recognition cue describing the question type that triggers it. Working block by block embeds the recognition habit that the two-second drill depends on.
Block 1 — Basic Conversions and Percentage Change (5 formulas)
The basic block is the gateway. These five formulas describe percentage as a fraction, the standard percentage change operation, and the fraction-to-percentage table that CAT setters embed in nearly every Arithmetic question. Recognition cue: any question that involves a direct conversion, a single percentage change, or a fraction-to-percentage swap.
| # | Formula | Use case |
|---|---|---|
| 1 | x% of y = (x / 100) × y | Direct percentage of a value. |
| 2 | Percentage change = ((new − old) / old) × 100 | Single increase or decrease. |
| 3 | x is what % of y: (x / y) × 100 | Ratio-as-percentage question stem. |
| 4 | x is what % more/less than y: ((x − y) / y) × 100 | Comparative percentage statement. |
| 5 | Fraction-to-% table: 1/8 = 12.5%, 1/7 = 14.28%, 1/6 = 16.67%, 1/9 = 11.11%, 1/12 = 8.33%, 1/11 = 9.09% | Mental conversion shortcuts. |
Block 2 — Successive Percentages and Multiplier Method (4 formulas)
The successive block is the highest-yield in CAT percentages. Two chained percentage changes are not the sum of the two changes. CAT setters exploit this with trap answers in nearly every successive percentage CAT question. Recognition cue: the question lists two or more percentage changes one after another, often with words like then, followed by, again, or further.
| # | Formula | Recognition cue |
|---|---|---|
| 6 | Net % change after +a% then +b% = a + b + (ab / 100) | Two successive increases. |
| 7 | Net % change after −a% then −b% = −a − b + (ab / 100) | Two successive decreases. |
| 8 | Net % change after +a% then −b% = a − b − (ab / 100) | Mixed increase and decrease. |
| 9 | Multiplier method: chain of changes = product of (1 ± r/100) | Three or more successive changes. |
Block 3 — Reverse Percentages and Restoration (4 formulas)
The reverse block is where most aspirants leak marks. A 25% increase is not undone by a 25% decrease. The symmetric trap is wired into nearly every reverse-percentage CAT question. Recognition cue: the question uses restore, original value, undo, back to, or asks for the percentage change required to reverse a previous change.
| # | Formula / Rule | Use case |
|---|---|---|
| 10 | To undo +x%: required decrease = (x / (100 + x)) × 100 % | Restoring after an increase. |
| 11 | To undo −x%: required increase = (x / (100 − x)) × 100 % | Restoring after a decrease. |
| 12 | If A is x% more than B, then B is (x / (100 + x)) × 100 % less than A | Bidirectional comparison. |
| 13 | If A is x% less than B, then B is (x / (100 − x)) × 100 % more than A | Bidirectional comparison. |
Block 4 — Percentage Applications and Word Problems (5 formulas)
The application block is where percentages plug into the rest of CAT Arithmetic. These five identities cover the recurring word-problem patterns: population growth, depreciation, marks and passing percentages, salary increments, and election margins. Recognition cue: a real-world word problem with a percentage applied across time, marks, votes, or quantities.
| # | Formula / Rule | Use case |
|---|---|---|
| 14 | Population after n years at r% growth = P(1 + r/100)n | Population growth. |
| 15 | Depreciated value after n years at r% = V(1 − r/100)n | Asset depreciation. |
| 16 | Passing marks = (pass% / 100) × total; failing margin = passing − obtained | Marks and passing problems. |
| 17 | Increased salary after multiple increments = S × (1 + r1/100)(1 + r2/100)… | Salary or rate hike chains. |
| 18 | Winning margin in % terms: (winner votes − loser votes) / total valid × 100 | Election or contest problems. |
Three Percentage Traps That Recur in CAT Papers
Three traps recur in CAT percentage questions. The first is direct addition of successive percentages. A 20% increase followed by a 20% decrease is not zero net change. The correct net is 20 minus 20 minus (400 / 100) = minus 4%. Forgetting the third term flips the answer into the trap option. The second trap is symmetric reverse thinking. A 25% increase is undone by a 20% decrease, not a 25% decrease. The reverse-percentage formula is asymmetric by design, and CAT setters lay trap options at the symmetric value.
The third trap is the base-shift problem. When two values are compared, the percentage change depends on which value is the base. A is 25% more than B does not imply B is 25% less than A. The correct statement is B is 20% less than A. Setters embed this asymmetry inside salary, population, and election problems where the base shift is easy to miss under time pressure.
20 Must-Solve CAT Percentage Questions
These 20 questions cover all four blocks of the cheatsheet. Each is tagged with the block and the formula it tests. The drill: solve under timed conditions, target under 75 seconds per question, and use the cheatsheet only for recall after attempting.
What is 35% of 480?
35% = 7/20. (7/20) × 480 = 7 × 24 = 168. Answer: 168
A value rises from 250 to 320. What is the percentage increase?
((320 − 250) / 250) × 100 = (70 / 250) × 100 = 28%. Answer: 28%
36 is what percent of 240?
(36 / 240) × 100 = 15%. Answer: 15%
A factory produced 1/7 more units this year than last. By what percentage did production rise?
1/7 = 14.28%. Answer: 14.28%
If A scores 480 and B scores 600, A scores what percent less than B?
((600 − 480) / 600) × 100 = 20%. Answer: 20%
A price rises by 20% and then by 25%. What is the net percentage change?
20 + 25 + (500 / 100) = 50%. Answer: 50%
A salary is cut by 10% and then again by 20%. Net percentage change?
−10 − 20 + (200 / 100) = −28%. Answer: 28% decrease
A value increases by 30% and then decreases by 20%. Net percentage change?
30 − 20 − (600 / 100) = 4%. Answer: 4% increase
A price rises by 10%, then by 20%, then drops by 25%. Net percentage change?
Multipliers: 1.10 × 1.20 × 0.75 = 0.99. Net = −1%. Answer: 1% decrease
A salary is raised by 25%. What percentage cut restores the original value?
(25 / 125) × 100 = 20%. Answer: 20%
A value drops by 20%. What increase restores it?
(20 / 80) × 100 = 25%. Answer: 25%
If A is 50% more than B, B is what percent less than A?
(50 / 150) × 100 = 33.33%. Answer: 33.33%
If A is 20% less than B, B is what percent more than A?
(20 / 80) × 100 = 25%. Answer: 25%
A town has 8000 residents, growing at 10% annually. Population after 2 years?
8000 × 1.10 × 1.10 = 8000 × 1.21 = 9680. Answer: 9680
A machine worth 50,000 depreciates 10% annually. Value after 3 years?
50000 × 0.93 = 50000 × 0.729 = 36450. Answer: 36,450
A student scores 220 out of 500 and fails by 30 marks. What is the passing percentage?
Passing marks = 220 + 30 = 250. Passing % = (250 / 500) × 100 = 50%. Answer: 50%
A salary of 40,000 gets a 10% hike then a 15% hike. New salary?
40000 × 1.10 × 1.15 = 40000 × 1.265 = 50,600. Answer: 50,600
In a two-candidate election, the winner gets 55% of 8000 valid votes. By how many votes did the winner win?
Margin in % = 55 − 45 = 10%. Vote margin = (10 / 100) × 8000 = 800. Answer: 800
A trader marks goods 40% above cost, then offers a 25% discount. What is the profit or loss percentage?
Multipliers: 1.40 × 0.75 = 1.05. Answer: 5% profit
A shopkeeper raised the price by 30% and later reduced it by 30%. What is the net effect on the original price?
30 − 30 − (900 / 100) = −9%. Answer: 9% decrease
Lock the Percentages Foundation Into Your CAT 2026 Plan
Percentages sits underneath six other Arithmetic topics. A diagnostic-driven plan puts this block in week one of CAT preparation so every downstream topic compounds instead of stalling.
Lock My Percentage Foundation BlockWhere Percentages Fit in the CAT 2026 Arithmetic Cluster
Percentages is the entry point to the Arithmetic cluster, which contributes 35 to 40% of CAT Quant weightage. The cluster sequence: percentages first, then Profit Loss and Discount, then Simple and Compound Interest, then Ratio and Proportion, then Time Speed Distance, then Time and Work. Every later topic borrows the percentage layer underneath. A 3 to 4 day study block, scheduled in week one of any CAT 2026 plan, builds the foundation that the remaining six weeks of Arithmetic stand on.
For a working professional with limited weekly hours, this 3 to 4 day block can stretch to a single week, which still places percentages in the first month of preparation. The Optima Learn CAT exam guide sequences the rest of the Arithmetic cluster topic by topic, and the CAT 2026 waitlist details page explains how the diagnostic-driven planner builds the cluster sequence around an aspirant's specific starting level.
Three Reflexes That Compress Percentage Solves to Under 30 Seconds
Once the 18 shortcuts are memorised, three reflexes separate aspirants who finish percentage questions in 30 seconds from those who take a minute and a half. Reflex one: fraction-first. Before any percentage calculation, convert the percentage to its nearest fraction. 14.28% becomes 1/7, 16.67% becomes 1/6. Calculation collapses from multiplication to division. Reflex two: multiplier-chain. For any chain of three or more changes, write the multipliers in a single line and multiply, rather than applying the successive formula three times. Reflex three: reverse-base check. Whenever the question says restore, original, undo, or back to, immediately write down the asymmetric reverse formula before reading further. These three install through timed drill, and the CAT preparation blogs library has companion cheatsheets on Quadratic Equations, Number System, and Time Speed Distance.
Common Doubts About Percentage Preparation for CAT 2026
How many percentage questions appear in CAT 2026?
Expect 1 to 2 direct CAT percentage questions plus 8 to 10 adjacent Arithmetic and Data Interpretation questions that lean on the same identities underneath. The compounded contribution is 8 to 12 marks per paper. Given that 18 shortcuts cover the topic, the return on a focused 3 to 4 day block is one of the highest in CAT preparation.
Is the multiplier method always faster than the successive formula?
For two changes, the successive formula a + b + (ab/100) is faster. For three or more changes, the multiplier method is faster. The split is roughly 60% of questions favour the successive formula and 40% favour multipliers, so both are worth automating. Switch on the fly based on the question stem.
Should I memorise the fraction-to-percentage table cold?
Yes, this is the single highest-leverage memorisation in CAT Arithmetic. Drill 1/n from n = 2 to n = 16, plus 1/20 and 1/25, for two minutes daily until each conversion fires in under one second. CAT setters embed these fractions in nearly every Arithmetic question, and the mental conversion alone saves five to ten seconds per question, which adds up across a 22-question section.
How do I revise the cheatsheet one week before CAT 2026?
A one-week revision plan: day one, re-read the 18-formula cheatsheet. Day two, drill the fraction-to-percentage table cold. Day three, drill the four successive percentage formulas. Day four, drill the four reverse percentage formulas. Day five, attempt 20 mixed-block questions under timed conditions. Day six, review every error and re-attempt. Day seven, scan the cheatsheet once for 15 minutes only before the exam, then leave it.
Final note. The CAT 2026 cheatsheet reduces to 18 shortcuts across four blocks, with the successive and reverse blocks carrying the most weight. The topic rewards recognition over computation, which is what most internet content gets wrong. Drill block by block, build the three reflexes, and the CAT score predictor alongside mocks will track the lift across Profit Loss, SI CI, and Data Interpretation downstream.
