Antyayordashake
To multiply two numbers whose units add to 10 and that share the same tens digit, multiply the tens digit by one more than itself for the front, and multiply the two units digits for the back. For 43 × 47: 4 × 5 = 20 and 3 × 7 = 21, giving 2021. It is the fastest pattern in the whole Vedic set.
This is the narrowest of the Vedic techniques and the most satisfying when it lands: a multiplication that looks like real work resolves in about two seconds. It is a close relative of the squaring rule for numbers ending in 5, which is simply this pattern with both units equal to 5.
Try it against the clock. Complementary Products 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.
The tens parts must be identical and the units must sum to exactly ten. 43 and 47 qualify; 43 and 57 do not. Checking takes a moment and stops the method being applied where it produces a wrong answer.
For 43 × 47, the leading part is 4, so compute 4 × 5 = 20. This is the front of the answer, and it is the same Ekadhikena step used for squaring numbers that end in 5.
3 × 7 = 21. Pad to two digits — 62 × 68 gives 42 and 16, that is 4216, and 61 × 69 gives 42 and 09, that is 4209. The pad is where the errors live.
When both units are 5, the two numbers are equal and the rule becomes the squaring shortcut: 75 × 75 is 7 × 8 = 56 then 5 × 5 = 25, giving 5625. One pattern, two uses.
| Pair | Applies? |
|---|---|
| 43 × 47 | Yes — same tens, units 3 + 7 = 10 |
| 62 × 68 | Yes — 2 + 8 = 10 |
| 75 × 75 | Yes — the squaring special case |
| 43 × 57 | No — different tens digits |
| 44 × 47 | No — units sum to 11 |
| 105 × 105 | Yes — leading part 10, units both 5 |
Generated by the same engine that mints the ComputePrep 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.
73 × 77 = ?
Units sum to 10, same lead — beat the clock.
81 × 89 = ?
Units sum to 10, same lead — beat the clock.
37 × 33 = ?
Units sum to 10, same lead — 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.
Both conditions are required. 43 × 57 looks similar and the method gives a confidently wrong answer, because nothing in the arithmetic signals that it does not apply.
61 × 69 gives a back part of 9, which must be written 09. Dropping the pad shifts the answer by a factor of ten.
The check should take under a second. If it does not resolve immediately, use crosswise multiplication and move on.
Only when the two numbers share the same leading part and their units digits add to exactly ten — 43 × 47, 62 × 68, 105 × 105. Both conditions must hold. If either fails, the crosswise method is the right choice.
It is the same rule. A number ending in 5 multiplied by itself has an identical leading part and units summing to ten, so 75 × 75 gives 7 × 8 = 56 and 5 × 5 = 25, or 5625. Learning one gives you the other for free.
Yes. The leading part can be any length, so 112 × 118 gives 11 × 12 = 132 and 2 × 8 = 16, that is 13216. The units must still sum to ten and everything before them must match.
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