Vedic maths
Seven shortcuts that turn four lines of paper into two steps
These are the seven techniques ComputePrep's Vedic path drills, one kind at a time, on a 15–45 second clock. Each is worked below — read it once, then practise it daily until it stops feeling like a trick. They are seven of the 16 sutras and 13 sub-sutras in the traditional canon — see the full list for what the other twenty-two cover and why they aren't drilled here.
Short answer for anyone in a hurry: the seven ComputePrep drills daily are Nikhilam (multiplying near 100), Ekadhikena and Yavadunam (squaring), Antyayordashake (units adding to 10), Sankalana-Vyavakalanabhyam (multiply through the midpoint), Urdhva-Tiryagbhyam (the general crosswise method), Paravartya Yojayet (dividing near a base) and Anurupyena (multiplying near a working base that isn't a power of 10). The other nine sutras and eleven sub-sutras solve algebra and calculus problems, not bank/SSC arithmetic — see why below.
1. Nikhilam — multiplying near a base
When to use it: both numbers sit close to 100 (or 10, 1000).
97 × 96
- Deficits from 100: 97 → −3, 96 → −4.
- Left part — cross-subtract: 97 − 4 = 93 (or 96 − 3 = 93; they always agree).
- Right part — multiply the deficits: 3 × 4 = 12.
- Join them: 93 | 12 → 9312.
The trap, and the one thing to drill: the right part must be exactly as wide as the base has zeros. 88 × 89 gives deficits 12 and 11, so the right part is 132 — three digits where only two fit. Carry the extra: 77 | 132 → 7700 + 132 = 7832. Writing 77132 is the classic error, and it is always sitting in ComputePrep's options waiting for you.
Start a timed Nikhilam drill →
2. Vedic squaring — Ekadhikena and Yavadunam
When to use it: the number ends in 5, or sits near a base.
Ends in 5 — Ekadhikena: take the part before the 5, multiply it by one more than itself, append 25.
75² → 7 × 8 = 56, append 25 → 5625.
85² → 8 × 9 = 72 → 7225.
Near a base — Yavadunam: subtract the deficit again, then append the deficit squared (same carry rule as Nikhilam).
96² → 96 − 4 = 92, 4² = 16 → 9216.
88² → 88 − 12 = 76, 12² = 144 → 7600 + 144 = 7744.
88² is the drill that matters — 98² never teaches you the carry.
Start a timed Vedic Squaring drill →
3. Complementary products — Antyayordashake
When to use it: the two numbers have the same leading part and their units digits add to 10.
43 × 47 — same tens (4), units 3 + 7 = 10.
- Left: 4 × 5 = 20 (the tens digit times one more than itself).
- Right: 3 × 7 = 21 (the units, padded to two digits).
- 20 | 21 → 2021.
Padding matters: 91 × 99 → 9 × 10 = 90, 1 × 9 = 09 → 9009, not 909.
Start a timed Complementary Products drill →
4. Difference of squares — Sankalana-Vyavakalanabhyam
When to use it: the two numbers are equally spaced around a round midpoint.
47 × 53 — midpoint 50, distance 3.
50² − 3² = 2500 − 9 = 2491.
68 × 72 — midpoint 70, distance 2: 4900 − 4 = 4896.
The error the options will offer you is m² + d². It is a plus sign that costs a mark.
Start a timed Difference of Squares drill →
5. Crosswise multiplication — Urdhva-Tiryagbhyam
When to use it: everything else. This is the general method — it multiplies any two numbers in one line, with no special condition.
23 × 41
- Units: 3 × 1 = 3.
- Cross: (2 × 1) + (3 × 4) = 14 → write 4, carry 1.
- Tens: 2 × 4 = 8, plus the carry → 9.
- 943.
The easy variant — × 11: first digit, then the neighbour sums, then the last digit. 43 × 11 → 4 | (4+3) | 3 = 473. With a carry: 87 × 11 → 8 | 15 | 7 → 957.
Start a timed Crosswise Multiplication drill →
6. Paravartya Yojayet — dividing by a number just above a base
When to use it: the divisor sits one more than a round base — 11 (one above 10), 101 (one above 100). ComputePrep drills the clean case, dividing by 11, where no digit position ever needs a borrow.
1234 ÷ 11 — base 10, divisor 11 = 10 + 1.
- Bring down the first digit as-is: 1 (first quotient digit).
- Multiply the last quotient digit by −1 and add it to the next dividend digit: 2 + (−1×1) = 1 (second quotient digit).
- Repeat: 3 + (−1×1) = 2 (third quotient digit).
- The last digit gives the remainder the same way: 4 + (−1×2) = 2.
- Quotient 112, remainder 2 — check: 112 × 11 + 2 = 1234.
It scales to any length: 123456 ÷ 11 runs the same left-to-right chain across six digits and gives quotient 11223, remainder 3.
Start a timed Paravartya Division drill →
7. Anurupyena — multiplying near a working base that isn't a power of 10
When to use it: both numbers sit close to a convenient number that is a simple fraction or multiple of a power of 10 — 50 (= 100 ÷ 2), 25 (= 100 ÷ 4) — rather than close to 10, 100 or 1000 directly. ComputePrep drills the clean case, where both numbers sit on the same side of the working base, which keeps the rescaling step a whole number every time.
46 × 48 — working base 50 = 100 ÷ 2.
- Deviations from 50: 46 → −4, 48 → −2.
- Cross-add for the raw left part: 46 − 2 = 44 (or 48 − 4 = 44).
- Rescale the left part for the working base: 50 is 100 ÷ 2, so divide by 2: 44 ÷ 2 = 22.
- Right part — multiply the deviations: (−4) × (−2) = 8, padded to two digits: 08.
- Join them: 22 | 08 → 2208.
Second check — 52 × 54: deviations +2 and +4, raw left 52 + 4 = 56, rescaled 56 ÷ 2 = 28, right part 2 × 4 = 08, joined: 2808.
Start a timed Anurupyena Multiplication drill →
Which shortcut applies? A ten-second decision
| What you see | Use | Example |
|---|---|---|
| Both numbers near 100 / 1000 | Nikhilam | 97 × 96 = 9312 |
| Number ends in 5, squared | Ekadhikena | 75² = 5625 |
| Number near a base, squared | Yavadunam | 88² = 7744 |
| Same tens, units add to 10 | Antyayordashake | 43 × 47 = 2021 |
| Equal distance from a round number | Difference of squares | 47 × 53 = 2491 |
| Multiplying by 11 | Neighbour sums | 87 × 11 = 957 |
| Anything else | Urdhva-Tiryagbhyam | 23 × 41 = 943 |
| Dividing by a base+1 number | Paravartya Yojayet | 1234 ÷ 11 = 112 r2 |
| Both near a non-decimal base, same side | Anurupyena | 46 × 48 = 2208 |
The full canon — 16 sutras, 13 sub-sutras, and why ComputePrep drills seven
Bharati Krishna Tirthaji's reconstruction of vedic mathematics lists 16 main sutras and 13 supporting sub-sutras — 29 formulas covering everything from mental arithmetic to solving simultaneous equations, factoring polynomials and calculus. Selection here is exam-driven, not completeness-driven: a technique earns a ComputePrep drill only when it turns into a single number an IBPS/SBI/SSC/Railway aspirant has to produce under a clock. Most of the rest solve a different kind of problem — an equation, not an arithmetic question — so there is no "correct answer among five options" to drill. Here is the complete list, for reference.
The 16 sutras
| # | Sutra | Meaning | On ComputePrep |
|---|---|---|---|
| 1 | Ekadhikena Purvena | By one more than the previous one | Vedic Squaring (ends-in-5) |
| 2 | Nikhilam Navatashcaramam Dashatah | All from 9 and the last from 10 | Nikhilam |
| 3 | Urdhva-Tiryagbhyam | Vertically and crosswise | Crosswise Multiplication |
| 4 | Paravartya Yojayet | Transpose and adjust | Paravartya Division |
| 5 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero | Not drilled — solves simultaneous equations |
| 6 | Anurupye Shunyamanyat | If one is in ratio, the other is zero | Not drilled — also equation-solving; a different technique from the Anurupyena sub-sutra below despite the similar name |
| 7 | Sankalana-Vyavakalanabhyam | By addition and by subtraction | Difference of Squares |
| 8 | Puranapuranabhyam | By the completion or non-completion | Not drilled — completing algebraic expressions |
| 9 | Chalana-Kalanabhyam | Differences and similarities | Not drilled — calculus and root-finding |
| 10 | Yaavadunam | Whatever the extent of its deficiency | Vedic Squaring (near-base) |
| 11 | Vyashtisamanstih | Part and whole | Not drilled — a general algebraic principle, no standalone arithmetic form |
| 12 | Shesanyankena Charamena | The remainders by the last digit | Not drilled — divisibility and recurring-decimal tests |
| 13 | Sopaantyadvayamantyam | The ultimate and twice the penultimate | Not drilled — a narrow quadratic-equation form |
| 14 | Ekanyunena Purvena | By one less than the previous one | Not drilled — multiplying by 9, 99, 999…; a close cousin of Nikhilam |
| 15 | Gunitasamuchyah | The product of the sum is the sum of the product | Not drilled — a factorization-verification identity |
| 16 | Gunakasamuchyah | The factors of the sum is the sum of the factors | Not drilled — a factorization identity |
The 13 sub-sutras
| # | Sub-sutra | Meaning | On ComputePrep |
|---|---|---|---|
| 1 | Anurupyena | Proportionately | Anurupyena Multiplication |
| 2 | Sisyate Sesasamjnah | The remainder remains constant | Not drilled |
| 3 | Adyamadyenantyamantyena | The first by the first and the last by the last | Not drilled — algebraic factorization |
| 4 | Kevalaih Saptakam Gunyat | For 7 the multiplicand is 143 | Not drilled — a fixed recipe for sevenths only |
| 5 | Vestanam | By osculation | Not drilled — divisibility testing |
| 6 | Yavadunam Tavadunam | Lessen by the deficiency | Not drilled — cube and higher-power shortcuts |
| 7 | Yavadunam Tavadunikritya Vargancha Yojayet | Lessen further, and set up the square of the deficiency | Not drilled — compound extension of Yavadunam |
| 8 | Antyayordashake'pi | Last totalling 10 | Complementary Products |
| 9 | Antyayoreva | Only the last terms | Not drilled — a narrower variant of the above |
| 10 | Samuccayagunitah | The sum of the products | Not drilled — algebraic identity check |
| 11 | Lopanasthapanabhyam | By alternate elimination and retention | Not drilled — factoring expressions in three or more variables |
| 12 | Vilokanam | By mere observation | Not drilled — a general principle, not a specific operation |
| 13 | Gunitasamuccayah Samuccayagunitah | The product of the sum is the sum of the products | Not drilled — algebraic identity, echoes sutra 15 above (a known overlap in Tirthaji's original text) |
Two names above look alike on purpose, not by our error: sub-sutra 1 (Anurupyena, "proportionately" — the working-base multiplication drilled on this page) and main sutra 6 (Anurupye Shunyamanyat, "if one is in ratio, the other is zero" — an equation-solving technique) are genuinely different formulas that share a root word. Vedic-maths sources online conflate them often enough that it's worth naming here.
Reading them is not the point
Every aspirant who has watched a vedic-maths video knows these exist. The gap between knowing a shortcut and reaching for it under a clock is where marks are lost, and it closes only with repetition against a timer.
That is the whole reason ComputePrep exists: the Vedic path rotates through these seven kinds, three difficulties a day, 15–45 seconds each, with the sutra steps shown after every single drill. It is free, and it takes about five minutes.
FAQ
What is the Nikhilam sutra?
A method for multiplying two numbers that sit close to a base like 100. You subtract crosswise to get the front part of the answer and multiply the two deficits to get the back part — 97 × 96 becomes 93 and 12, joined into 9312, without a single long-multiplication line.
How do you square a number that ends in 5?
Take the digits before the 5, multiply that number by one more than itself, and append 25. For 75²: 7 × 8 = 56, so the answer is 5625. This is Ekadhikena, and it works for any number of digits ending in 5.
What is Antyayordashake (complementary products)?
A shortcut for two numbers that share the same leading digits and whose units digits add to 10 — 43 × 47, for example. Multiply the leading part by one more than itself for the front (4 × 5 = 20), multiply the units for the back (3 × 7 = 21, padded to two digits), and join them: 2021.
Are vedic maths tricks actually worth learning for bank and SSC exams?
Only the ones that match how the paper actually sets its numbers — which is why this page drills seven sutras, not the dozens sometimes listed online (the full 16-sutra, 13-sub-sutra canon is below, for reference). Knowing a shortcut and reaching for it under a 15–45 second clock are different skills; the second one only comes from timed repetition, which is the whole reason ComputePrep exists.
How does Paravartya Yojayet help with division?
It turns division by a number just above a base (like 11, just above 10) into a left-to-right chain of small multiplications and additions instead of long division. For 1234 ÷ 11: bring down 1, multiply by −1 and add to each next digit in turn, reading off quotient 112 with remainder 2. It scales cleanly to any dividend length.
What is Anurupyena, and why isn't there a timed drill for it yet?
Anurupyena multiplies near a convenient working base other than a power of 10 — 50, for instance, treated as 100 ÷ 2. It is genuinely useful, but the general case (numbers straddling the base on opposite sides) needs a fractional-rescaling step we want to teach carefully before it appears as a timed, auto-scored drill. For now it is here as a worked preview, restricted to the clean case where both numbers sit on the same side of the base.
Take them with you: the free Vedic Speed Kit (PDF) packs all seven techniques with engine-verified worked steps, 28 practice problems and the speed tables — yours to keep and forward.
The other half of the paper. Speed handles quant; the reasoning section needs a different muscle. Our sister product Deduce is a daily reasoning puzzle across 29 reasoning types — same makers, same aspirants, same five-minute habit.