CAT 2026 Percentage Tricks: Fraction Table + 15 PYQs
A speed-first percentage formula reference for CAT 2026 aspirants, closing the percentage-foundation gap in the Optima Learn arithmetic cluster. Features the canonical 15-entry percentage-to-fraction conversion table (1/2 through 1/12 plus key multiples like 5/8 and 7/8), the 4 core percentage formulas (basic, change, successive, multiplier), the more-than vs less-than asymmetry trap, 5 speed-up tricks that save 60 to 90 seconds per arithmetic question, and 15 solved PYQ-style problems across the 5 dominant CAT percentage problem types.
CAT 2026 Percentage Tricks: Fraction Table + 15 PYQs
Percentages are the foundation of almost every CAT Quant arithmetic question. Time-speed-distance, profit-loss, simple and compound interest, mixtures, and even some DI questions all reduce to percentage applications. The CAT QA section has 4 to 6 directly percentage-based questions per cycle plus 5 to 8 questions that use percentages as intermediate steps. Aspirants who have not internalised the standard percentage-to-fraction conversions lose 60 to 90 seconds per arithmetic question to decimal multiplication. Across a 40-minute QA section, that gap is 3 to 5 questions worth of time — the difference between a 75 and 90 percentile QA score.
This guide is the speed-first reference for percentage formulas CAT 2026: the fraction conversion table from 1/2 to 1/12 plus key multiples, the successive percentage change formula with worked examples, the more-than vs less-than asymmetry that traps 30 to 40 percent of aspirants, and 15 solved past-year-style problems. Memorise the table once; use it for the next 6 months.
The percentage-to-fraction conversion table is the single highest-ROI CAT Quant memorisation. Standard: 1/2 = 50, 1/3 = 33.33, 1/4 = 25, 1/5 = 20, 1/6 = 16.67, 1/7 = 14.28, 1/8 = 12.5, 1/9 = 11.11, 1/10 = 10, 1/11 = 9.09, 1/12 = 8.33 percent. Plus multiples: 2/3 = 66.67, 3/4 = 75, 5/8 = 62.5, 7/8 = 87.5 percent. Successive percentage change formula: net % = a + b + ab/100. More-than vs less-than asymmetry: if A is x percent more than B, then B is 100x/(100+x) percent less than A, not x percent less. 15 PYQ-style problems below drill the speed-up.
The Percentage-to-Fraction Conversion Table
This table is the single most important asset for CAT Quant speed. Print it, screenshot it, share it in your CAT WhatsApp group — whatever it takes. Memorising the table eliminates decimal multiplication for roughly 60 percent of CAT percentage questions. The table reads as: this fraction equals this percent, and the inverse multiplier is what you use when computing "find x percent of N".
| Fraction | Percent | "Find x% of N" multiplier | Speed example |
|---|---|---|---|
| 1/2 | 50% | ÷ 2 | 50% of 70 = 35 |
| 1/3 | 33.33% | ÷ 3 | 33.33% of 90 = 30 |
| 1/4 | 25% | ÷ 4 | 25% of 80 = 20 |
| 1/5 | 20% | ÷ 5 | 20% of 75 = 15 |
| 1/6 | 16.67% | ÷ 6 | 16.67% of 120 = 20 |
| 1/7 | 14.28% | ÷ 7 | 14.28% of 84 = 12 |
| 1/8 | 12.5% | ÷ 8 | 12.5% of 96 = 12 |
| 1/9 | 11.11% | ÷ 9 | 11.11% of 90 = 10 |
| 1/10 | 10% | ÷ 10 | 10% of 250 = 25 |
| 1/11 | 9.09% | ÷ 11 | 9.09% of 110 = 10 |
| 1/12 | 8.33% | ÷ 12 | 8.33% of 96 = 8 |
| 2/3 | 66.67% | × 2/3 | 66.67% of 60 = 40 |
| 3/4 | 75% | × 3/4 | 75% of 80 = 60 |
| 3/5 | 60% | × 3/5 | 60% of 50 = 30 |
| 5/8 | 62.5% | × 5/8 | 62.5% of 80 = 50 |
| 7/8 | 87.5% | × 7/8 | 87.5% of 80 = 70 |
The high-yield rows (1/2 through 1/12) get the most CAT exposure because they cover all the common percentages from 8 to 50. The multiples (2/3, 3/4, 5/8, 7/8) cover the high-percentage region (60 to 90) where most discount and profit-loss problems sit. The profit and loss formulas guide uses this table extensively for markup, discount, and successive discount calculations.
The 4 Core Percentage Formulas
Four formulas cover roughly 90 percent of CAT percentage applications. The remaining 10 percent are combinations or exotic phrasings of these four.
x percent of N
x% of N = (x / 100) × N
The fundamental definition. In practice, convert x percent into a fraction using the conversion table, then multiply. Example: 12.5 percent of 80 equals (1/8) times 80 equals 10. Decimal version (0.125 × 80) takes 30 seconds; fraction version takes 5 seconds.
Percentage change from A to B
% change = ((B − A) / A) × 100
Positive for increase, negative for decrease. Critical caveat: the more-than vs less-than asymmetry. If A is 25 percent more than B, then B is (100 × 25) / (100 + 25) = 20 percent less than A, not 25 percent less. The fraction multiplier version makes this obvious: A = 5/4 × B means B = 4/5 × A, so B is 1 minus 4/5 = 1/5 = 20 percent less.
Net change after two successive percentage changes
Net % = a + b + (ab / 100)
Where a and b are positive for increase, negative for decrease. Example: a 15 percent discount followed by a 10 percent discount produces net change of −15 + −10 + ((−15)(−10)/100) = −25 + 1.5 = −23.5 percent. Net 23.5 percent discount, not 25 percent. For three or more successive changes, apply pairwise.
Multiplier for successive changes
Final = Initial × (1 + a/100) × (1 + b/100) × ...
Exact for any number of successive changes. Slightly slower than the a + b + ab/100 formula for two changes but more reliable for three or more. Example: salary doubles via 20 percent, 15 percent, 10 percent successive hikes? Multiplier = 1.2 × 1.15 × 1.10 = 1.518. So salary increases by 51.8 percent.
Five Percentage Speed-Up Tricks
Five disciplined habits drop CAT percentage solve time by 40 to 60 percent for an aspirant who has internalised the fraction conversion table:
- Convert before computing. See "20 percent of 75"; write 75 ÷ 5 = 15, not 0.20 × 75. The fraction-multiplier version is 3 to 5 times faster.
- Use equivalent-ratio shortcut. "A is 25 percent more than B" becomes A:B = 5:4. Most A-vs-B comparison questions solve in 10 seconds once the ratio is written.
- Chain fractions for percent-of-percent. "60 percent of 75 percent of N" = (3/5) × (3/4) × N = (9/20) × N = 0.45N. Direct multiplication of fractions is faster than two decimal steps.
- Memorise the more-than/less-than asymmetry. If A is x percent more than B, B is 100x/(100+x) percent less. Common values: 25 percent more ↔ 20 percent less; 33.33 percent more ↔ 25 percent less; 50 percent more ↔ 33.33 percent less.
- Verify with magnitude check. If a 20 percent increase followed by a 20 percent decrease produces an answer that is the original, you have made an error. The correct answer is the original times 0.96 (a 4 percent net decrease).
The single highest-leverage memorisation in CAT Quant is the percentage-to-fraction conversion table for 1/2 through 1/12. Print it on a single A4 page, stick it next to your study desk, and review it at the start of every Quant session for 4 weeks. By week 5 it becomes reflex, and from then on percentage-based questions across profit-loss, simple-compound interest, and mixtures solve in half the previous time.
15 Solved PYQ-Style Percentage Problems
The 15 problems below span the 5 dominant percentage problem types — change, percent-of-percent, percent-of-base, mixture, and profit-loss application. Each solution shows the fraction-multiplier shortcut explicitly.
Type 1: Percentage Change (3 problems)
A's salary is 25 percent more than B's. By what percent is B's salary less than A's?
Solution: A is 25% more than B means A = 5/4 × B. So B = 4/5 × A, which means B is 1/5 = 20 percent less than A. Answer: 20 percent.
A number is increased by 40 percent and then decreased by 30 percent. Find the net percentage change.
Solution: Net % = 40 + (−30) + (40 × −30)/100 = 10 + −12 = −2. Answer: 2 percent decrease.
A salary increases by 20 percent in year 1 and another 25 percent in year 2. Find total percentage increase.
Solution: Multiplier: 1.20 × 1.25 = 1.50. So 50 percent increase. Answer: 50 percent.
Type 2: Percent-of-Percent (3 problems)
If 30 percent of A equals 25 percent of B, find A:B.
Solution: 0.3 A = 0.25 B means A/B = 25/30 = 5/6. Answer: A:B = 5:6.
75 percent of 60 percent of N equals 90. Find N.
Solution: (3/4) × (3/5) × N = 90 means (9/20) × N = 90 means N = 200. Answer: 200.
A discount of 20 percent followed by another 15 percent results in a net discount of how much?
Solution: Multiplier: 0.80 × 0.85 = 0.68. So net discount = 1 − 0.68 = 32 percent. Answer: 32 percent.
Type 3: Percent-of-Base (3 problems)
12.5 percent of a number is 30. Find the number.
Solution: 12.5% = 1/8. So (1/8) × N = 30 means N = 240. Answer: 240.
What percent of 80 is 12?
Solution: 12/80 = 3/20 = 15 percent. Answer: 15 percent.
A spends 60 percent of his income on rent and food, 15 percent on travel, saves the rest. If savings = 5000, find income.
Solution: Savings = 100 − 60 − 15 = 25 percent. 25% of income = 5000 means income = 20,000. Answer: 20,000.
Type 4: Mixture as Percent (3 problems)
A jar of 80 litres contains 30 percent milk. How many litres of milk must be added to make milk 50 percent?
Solution: Initial milk = 24 L, water = 56 L. Add x litres milk. New milk = 24 + x; total = 80 + x. (24 + x)/(80 + x) = 1/2. 48 + 2x = 80 + x means x = 32. Answer: 32 litres.
Mix 25 percent salt solution with 60 percent salt solution to get 70 litres of 40 percent solution. How much of each?
Solution: Let q1 = 25%, q2 = 60%. q1 + q2 = 70 and 0.25 q1 + 0.60 q2 = 28. Solve: q2 = (28 − 17.5)/0.35 = 30. q1 = 40. Answer: 40 L of 25%, 30 L of 60%.
Sugar solution is 40 percent. To reduce concentration to 25 percent, what fraction of solution should be replaced with water?
Solution: Concentration ratio: 25/40 = 5/8. So 5/8 of original sugar remains, meaning 3/8 of solution replaced with water. Answer: 3/8.
Type 5: Profit-Loss Application (3 problems)
An item is marked up 40 percent then sold at 20 percent discount. Find net profit percent.
Solution: Net = 40 + (−20) + (40 × −20)/100 = 20 + −8 = 12. Answer: 12 percent profit.
CP is 80, SP is 120. Profit percent?
Solution: Profit = 40, profit % = 40/80 = 1/2 = 50 percent. Answer: 50 percent.
A shopkeeper marks up cost price by 25 percent and offers 10 percent discount on MP. Find profit percent.
Solution: Net = 25 + (−10) + (25 × −10)/100 = 15 + −2.5 = 12.5 percent. Answer: 12.5 percent profit.
Want a CAT 2026 Quant plan that drills the percentage-to-fraction conversion table to reflex level?
Build My CAT Quant PlanCommon Percentage Mistakes (and Their 5-Second Fixes)
Three patterns account for 60 to 70 percent of percentage errors in CAT mocks:
- The more-than/less-than symmetry assumption. Aspirants assume "A is 25 percent more than B" means "B is 25 percent less than A". It does not (the correct value is 20 percent less). Fix: memorise the asymmetry table for common values.
- Wrong base for percentage change. Computing percentage change with respect to the new value instead of the original. Always divide by the original.
- Decimal multiplication when fraction conversion exists. Computing 12.5 percent of 96 as 0.125 × 96 instead of 96 / 8. The decimal version takes 30 seconds; the fraction version takes 5.
Aspirants memorise the percent-to-decimal version (12.5 percent = 0.125) and use it everywhere. The percent-to-fraction version (12.5 percent = 1/8) is 3 to 5 times faster for CAT-style arithmetic because most CAT problems have integer answers reachable by integer division. Train both representations but lead with the fraction version in mocks.
- Memorise the 15-entry percentage-to-fraction conversion table for 1/2 through 1/12 plus key multiples.
- Convert before computing. Fraction multipliers are 3 to 5 times faster than decimal.
- More-than vs less-than is asymmetric. Memorise the common asymmetry pairs (25/20, 33.33/25, 50/33.33).
- Successive percentage change: net % = a + b + ab/100. Apply pairwise for three or more.
- For mixed percentage problems, chain fractions directly: 60 percent of 75 percent = 9/20.
- Magnitude check: 20 percent up then 20 percent down equals 4 percent net down, not zero.
- Drill 30 to 40 percentage problems across the 5 problem types over 5 to 7 days for reflex-level speed.
Percentages are the foundation of CAT arithmetic. Master the fraction conversion table once, save 3 to 5 questions worth of time in every QA section after.
Get a CAT 2026 Quant Plan That Drills Percentages
The Optima Learn CAT 2026 waitlist builds a personalised plan that includes the 15-entry fraction conversion table memorisation, 30-problem drill across the 5 percentage problem types, and the arithmetic cluster (profit-loss, simple-compound interest, ratio-proportion) that compounds the percentage savings.
Build My CAT Quant Plan
Optima Learn Editorial Team
CAT preparation specialists publishing structured guides on the CAT exam, CAT Quant topics, IIM admissions, and MBA entrance prep. We track CAT arithmetic per-question time distributions and the marginal lift from fraction-conversion drilling across aspirant cohorts.
Drill these Quant concepts on real PYQs
20,000+ tagged CAT Quant PYQs, sorted by difficulty and topic.