Anurupyena
To multiply numbers near 50, treat 50 as half of 100. Note each number's deviation from 50, cross-add one number with the other's deviation for a raw left part, then divide that by 2 to rescale for the smaller base. Multiply the two deviations for the right part, pad it to two digits, and join the two halves together.
Anurupyena is nikhilam's cousin for a working base that is not 100 itself, but a simple fraction of it. 50 is the common case in exam questions, and the extra rescale step is exactly what separates this technique from nikhilam — everything else about the crosswise structure is the same.
Try it against the clock. Anurupyena Multiplication runs at 15s easy, 20s medium and 30s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
54 is 4 above 50, and 56 is 6 above. Anurupyena only applies when both deviations sit on the same side of the base — both above 50 or both below. Mixed signs break the method, because the rescale step stops landing on a whole number.
Add one number to the other's deviation: 54 + 6 = 60, or equivalently 56 + 4 = 60 — both routes agree, a free check. This raw figure is not the answer's left part yet.
50 is 100 ÷ 2, so divide the raw left part by 2: 60 ÷ 2 = 30. This division is the step every other Vedic multiplication skips, and it is the one this method is built around.
4 × 6 = 24, padded to two digits and joined to the left part: 30 | 24 gives 3024. A single-digit product like 4 keeps its leading zero as 04, exactly as in nikhilam.
| Situation | What to do |
|---|---|
| Both numbers above 50 (54, 56) | Cross-add, divide by 2 for the left part: 30|24 → 3024 |
| Both numbers below 50 (46, 48) | Same steps, deviations negative: 22|08 → 2208 |
| One number is exactly 50 | One deviation is 0 — the right part is 0, the left part is just the other number |
| Deviations multiply past two digits | The right part overflows and carries into the left part, same as nikhilam |
Generated by the same engine that mints the Quant Daily daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
46 × 44 = ?
Multiplying near a working base — beat the clock.
54 × 54 = ?
Multiplying near a working base — beat the clock.
46 × 48 = ?
Multiplying near a working base — beat the clock.
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
The raw crosswise sum is not the left part — it must be halved first. Forgetting the ÷2 step gives an answer exactly twice too large in the tens-and-above place.
One number above 50 and one below makes the deviations opposite signs, and the rescale stops landing on a whole number. Nikhilam near a base of 100, or plain crosswise multiplication, is the right tool instead.
52 × 52 has deviations 2 and 2, so the right part is 2 × 2 = 4 — which must be written 04, not 4. Written as 4, the join reads 274 instead of 2704.
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
Because 50 is half of 100. The deficits are measured from 50 but the place value belongs to the hundreds column, so the front has to be divided by two. For 48 × 47: the front is 48 − 3 = 45, half of that is 22 with a half left over, and the back is 3 × 2 = 06.
It is half a hundred, so add 50 to the back. Continuing 48 × 47: the front 45 halves to 22 with 0.5 remaining, so the back becomes 06 + 50 = 56 and the product is 2256. Dropping that half loses exactly 50, which is why the answer looks so nearly right.
The right-hand part is always two digits. For 49 × 48 the front is 47, which halves to 23 and a half, and the back is 1 × 2 = 2, written 02, plus 50 for the leftover half, giving 52. The product is 2352, and writing 2 instead of 02 collapses it to three digits.
Anurupyena treats 50 as a working base half of 100. Find each number's deviation from 50, cross-add one number with the other's deviation, then divide that sum by 2 to rescale it — because 50 is 100 divided by 2. Multiply the two deviations for the right part, pad it to two digits, and join the two halves.
Because working with a base of 50 instead of 100 means every crosswise result comes out twice as large as it should. Dividing by 2 corrects for that — skip it and the answer is exactly double what it should be in the leading digits.
No. Both numbers need to sit on the same side of 50 — both above it or both below it — or the deviations carry opposite signs and the halving step stops landing on a whole number. Use nikhilam near a base of 100, or ordinary crosswise multiplication, instead.
Nikhilam multiplies near a base like 100 directly. Anurupyena is for numbers near a convenient working base that is a simple fraction of 100 — 50 is half of it — so an extra rescaling step is needed after the crosswise addition. The right-hand part, multiplying the two deviations, works the same way in both.
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