Quantitative Aptitude Formulas Cheat Sheet 2026 (Complete Reference)
Complete quantitative aptitude formula cheat sheet for 2026: every key formula across percentages, profit-loss, ratios, time-work, TSD, interest, mensuration, and more.
What changed in 2026 drives
Mass-recruiter offer letters are flatter for 2026 batch - the 4-5 LPA ASE band has barely budged in three years while inflation eats real wages. Premium tracks (Digital, Pro, Elite, Specialist) are still where the differential lives, and they are entirely test-driven. If you are aiming higher than the default offer, the coding round is not optional pageantry - it is the entire interview.
What I'd actually study for this
- 01Two solid coding-round answers (1 medium-hard DSA each, with edge-case discussion) > five half-baked ones
- 02One real project you can defend end-to-end - file paths, design decisions, and what you would change
- 03One DBMS schema you actually built (not a textbook ER diagram), with at least 3 join-heavy queries written from memory
- 04Three behavioural STAR stories: failure recovered, conflict handled, ownership taken
Where most candidates trip up
The single biggest mistake is treating company-specific guides as primary prep and DSA as secondary. It is the opposite. Mass recruiters use the test as a filter, but premium tracks at every IT services company use coding to allocate offer band. Spend 70% of prep time on DSA + system fundamentals, 20% on company-specific patterns, 10% on HR rehearsal. Reverse that ratio and you collect the default offer.
Editorial commentary by Aditya Sharma · written for PapersAdda · not generated, not aggregated.
Last Updated: June 2026
This is a complete formula reference for placement quantitative aptitude, organized by topic. Candidates report that instant formula recall is what separates a fast solver from a slow one, since the arithmetic in placement tests is standard but the clock is tight. Review this sheet daily and test yourself by reproducing each formula from memory.
Percentages
| Concept | Formula |
|---|---|
| x% of y | (x/100) times y |
| What % is a of b | (a/b) times 100 |
| Percentage increase | (increase / original) times 100 |
| Percentage decrease | (decrease / original) times 100 |
| Successive change a% then b% | a + b + (ab/100) |
| Price rise p%, keep spend equal | reduce consumption by p/(100+p) times 100 |
Profit and Loss
| Concept | Formula |
|---|---|
| Profit | SP minus CP |
| Loss | CP minus SP |
| Profit % | (Profit / CP) times 100 |
| Loss % | (Loss / CP) times 100 |
| SP at profit % | CP times (100 + profit%)/100 |
| SP at loss % | CP times (100 - loss%)/100 |
| Same SP, one +x% one -x% | always a loss of (x/10)% squared |
| Discount % | (MP - SP)/MP times 100 |
Ratio and Proportion
| Concept | Formula |
|---|---|
| a:b = c:d means | ad = bc |
| Combine a:b and b:c | scale to common b, then a:b:c |
| Divide N in ratio p:q | shares N times p/(p+q) and N times q/(p+q) |
| Mean proportional of a and b | square root of ab |
Averages
| Concept | Formula |
|---|---|
| Average | sum of values / count |
| New average after adding a value | (old sum + new value)/(count + 1) |
| Average of first n natural numbers | (n+1)/2 |
| Average of consecutive numbers | average of first and last |
Time and Work
| Concept | Formula |
|---|---|
| Work rate | 1 / days to finish |
| Combined rate | sum of individual rates |
| Days together | 1 / combined rate |
| Pipes (fill and leak) | net rate = fill rate minus leak rate |
| Efficiency ratio | inverse of time ratio |
Time, Speed, Distance
| Concept | Formula |
|---|---|
| Distance | speed times time |
| Speed | distance / time |
| km/hr to m/s | times 5/18 |
| m/s to km/hr | times 18/5 |
| Train crossing platform | time = (train + platform length)/speed |
| Downstream speed | boat + stream |
| Upstream speed | boat minus stream |
| Average speed (equal distance) | 2ab/(a+b) |
Simple and Compound Interest
| Concept | Formula |
|---|---|
| Simple interest | P times R times T / 100 |
| Amount (SI) | P + SI |
| Compound amount | P times (1 + R/100) to the power T |
| Compound interest | amount minus P |
| CI minus SI for 2 years | P times (R/100) squared |
| Doubling at SI | rate times time = 100 |
Number System
| Concept | Formula |
|---|---|
| Product of two numbers | LCM times HCF |
| Sum of first n natural numbers | n(n+1)/2 |
| Sum of first n odd numbers | n squared |
| Sum of first n even numbers | n(n+1) |
| Sum of squares 1 to n | n(n+1)(2n+1)/6 |
| Divisibility by 3 | digit sum divisible by 3 |
| Divisibility by 9 | digit sum divisible by 9 |
| Divisibility by 11 | alternating digit sum divisible by 11 |
Mensuration
| Shape | Key Formula |
|---|---|
| Rectangle area | length times breadth |
| Rectangle perimeter | 2(length + breadth) |
| Square area | side squared |
| Triangle area | half times base times height |
| Circle area | pi times r squared |
| Circle circumference | 2 times pi times r |
| Cube volume | side cubed |
| Cuboid volume | length times breadth times height |
| Cylinder volume | pi times r squared times h |
| Sphere volume | four-thirds times pi times r cubed |
Permutation and Probability
| Concept | Formula |
|---|---|
| Permutation nPr | n! / (n-r)! |
| Combination nCr | n! / (r! times (n-r)!) |
| Circular arrangement | (n-1)! |
| Probability | favourable / total outcomes |
| At least one | 1 minus probability of none |
Clocks and Calendars
| Concept | Formula |
|---|---|
| Angle of hour hand | 30 times hours plus 0.5 times minutes |
| Angle of minute hand | 6 times minutes |
| Angle between hands | absolute difference of the two angles |
| Odd days in a normal year | 1 |
| Odd days in a leap year | 2 |
Numbers Worth Memorizing
| Set | Values |
|---|---|
| Squares 1 to 20 | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 |
| Squares 21 to 30 | 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 |
| Cubes 1 to 15 | 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375 |
| Fraction to percent | 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%, 1/9 = 11.11% |
Why These Formula Families Matter Most
Not all formulas carry equal weight in placement tests. Candidates consistently report that six families dominate the quantitative section, and understanding why helps you prioritize revision.
Percentages underpin almost everything, because profit and loss, discount, data interpretation, and population growth are all percentage problems in disguise. Mastering percentage change, successive change, and the consumption-reduction formula pays off across multiple topics at once. Profit and loss is the most directly tested commercial-math family, and the same-selling-price loss trick alone appears in many tests. Ratios and proportion are the connective tissue of mixture, partnership, and age problems, so ratio fluency unlocks several topics. Time and work, including pipes and cisterns, is a high-frequency family where the combined-rate method solves nearly every variant. Time, speed, and distance, with its train and boat sub-types, is among the most tested topics, and the average-speed formula is a perennial trap. Simple and compound interest rounds out the core six, with the two-year CI-minus-SI shortcut being a frequent quick win.
The remaining families, mensuration, number system, permutation and probability, and clocks and calendars, appear less often but are worth knowing because they are formula-pure: once you recall the formula, the answer is immediate. The strategic approach is to make the core six automatic first, then layer in the formula-pure families so that no question type catches you without its formula ready.
How To Use This Sheet
Candidates report that the formula sheet is only useful if you can reproduce it without looking. The practical method is spaced recall: review one or two sections per day, then close the sheet and write the formulas from memory. Mark the ones you miss and revisit them. The goal is that in the test, classifying a question instantly triggers the right formula. Pair this sheet with the topic-wise solved examples to see each formula in action, since formula plus worked application is what builds durable recall.
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Frequently Asked Questions
Which quantitative formulas are most important for placements?
Candidates report percentages, profit and loss, ratios, time and work, time-speed-distance, and simple and compound interest as the highest-frequency formula sets in TCS, Infosys, and Wipro quantitative sections. Master these six families first, since they cover the majority of questions.
How should I use a formula cheat sheet?
Review it daily in short sessions until recall is instant, then test yourself by writing formulas from memory. Candidates report that the goal is not reading the sheet but being able to reproduce each formula without looking, so that in the test the formula appears the moment you classify the question.
Do I need to memorize squares and cubes?
Yes. Candidates report that knowing squares up to 30 and cubes up to 15 saves significant time on number-system, mensuration, and series questions. These appear often enough that instant recall is a genuine speed advantage in a timed test.
Methodology applied to this articlelast verified 8 Jun 2026
- No fabricated salary numbers or success rates. If we quote a range, it's sourced.
- No noun-substituted templates. This article was not generated by swapping company names in a stock prompt.
- No paid placements, sponsored coaching links, or affiliate-shilled course pushes.
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