# Vedic maths shortcuts for bank & SSC exams — 7 sutras, worked examples

> The vedic-maths shortcuts ComputePrep drills daily, each worked step by step: Nikhilam (97 x 96 in two steps), vedic squaring (75² and 88²), complementary products (43 x 47), difference of squares (47 x 53), crosswise multiplication, Paravartya division (1234 ÷ 11) and Anurupyena working-base multiplication (46 x 48) — plus the full 16-sutra, 13-sub-sutra reference list for anyone curious what the rest cover. Free daily timed practice.

Source: https://computeprep.com/vedic-maths

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Vedic maths

## Seven shortcuts that turn four lines of paper into two steps

These are the seven techniques ComputePrep's [Vedic path](https://computeprep.com/drill-types) 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 →](https://computeprep.com/?drill=nikhilam&src=seo-vedic-hub-nikhilam)

### 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 →](https://computeprep.com/?drill=vedic_squaring&src=seo-vedic-hub-squaring)

### 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 →](https://computeprep.com/?drill=complementary_products&src=seo-vedic-hub-complementary)

### 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 →](https://computeprep.com/?drill=difference_of_squares&src=seo-vedic-hub-difference)

### 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 →](https://computeprep.com/?drill=urdhva_multiplication&src=seo-vedic-hub-crosswise)

### 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 →](https://computeprep.com/?drill=paravartya_division&src=seo-vedic-hub-paravartya)

### 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 →](https://computeprep.com/?drill=anurupyena_multiplication&src=seo-vedic-hub-anurupyena)

### 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)](https://computeprep.com/speed-kit) 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](https://deducepuzzles.com) is a daily reasoning puzzle across
 [29 reasoning types](https://deducepuzzles.com/reasoning-puzzle-types) — same makers, same aspirants, same five-minute habit.