In-Depth Tutorial
A formal, accessible 800–1000 word walkthrough of this topic, written for the serious aspirant. Switch to हिन्दी using the toggle on the right.
Why Multiplication Is the Highest-Value Vedic Skill
Multiplication is the single most frequent operation in any Quantitative Aptitude paper. Out of every twenty-five questions in a Banking Prelims paper or thirty questions in a Staff Selection Commission paper, between fifteen and eighteen require at least one multiplication step. The candidate who can multiply a two-digit pair in seven seconds rather than twenty-five seconds gains a cumulative advantage of three to five minutes per paper, which is exactly the time differential that separates aspirants above the cut-off from aspirants below it.
Vedic multiplication is built around two principal Sutras — Nikhilam Navatashcaramam Dashatah and Urdhva-Tiryagbhyam — supported by three special-case techniques for multiplication by eleven, by powers of nine, and by five and its multiples. Together these five methods cover essentially every multiplication situation that arises in competitive examinations.
Nikhilam — Multiplication Near a Base
Nikhilam, which translates as 'all from nine and the last from ten,' is the technique of choice when both numbers being multiplied are close to a base of ten, hundred, thousand or any higher power of ten. The base is the nearest such power, and the deficiency or surplus is the signed distance of each number from that base. The two-step procedure is simple. First, write the two deficiencies in a column to the right; their product, padded to as many digits as the base has zeros, is the right side of the answer. Second, write either number minus the other number's deficiency on the left.
Consider 96 × 92. Base 100; deficiencies 4 and 8. Right side 4 × 8 = 32. Left side 96 − 8 = 88 or equivalently 92 − 4 = 88. Answer 8832. Consider 103 × 108. Base 100; surpluses 3 and 8. Right side 3 × 8 = 24. Left side 103 + 8 = 111 or 108 + 3 = 111. Answer 11124. The same procedure works when one number is above and the other below the base, with appropriate sign treatment of the deficiencies. With twenty practice problems the technique becomes automatic.
Urdhva-Tiryagbhyam — Vertically and Crosswise
Urdhva-Tiryagbhyam is the general multiplication technique. It works for every pair of numbers regardless of their proximity to a base, and it produces the answer in a single horizontal line. For two two-digit numbers ab × cd, three columns are computed: the right column is bd, the middle column is ad + bc, and the left column is ac. Each column is a place value, and carries propagate from right to left.
Consider 23 × 14. Right column 3 × 4 = 12; middle column 2 × 4 + 3 × 1 = 11; left column 2 × 1 = 2. Writing 2, 11, 12 with carries gives 322. For three-digit numbers abc × def, five columns are computed using a slightly extended pattern of vertical and crosswise products. The same logic extends indefinitely. Once the candidate has practised the two-digit and three-digit forms on twenty problems each, any multiplication on the examination becomes a matter of writing three or five small products and adding the carries.
Multiplication by Eleven — A Three-Second Trick
Multiplication by eleven uses the Antyayoreva pattern. For a two-digit number ab, the answer is a, a+b, b — that is, the digits of the original number with their sum inserted in the middle. For 23 × 11, the digits are 2 and 3 with sum 5, giving 253. For 47 × 11, the digits are 4 and 7 with sum 11; since the middle is more than nine, we carry: 4+1, 1, 7 → 5, 1, 7 → 517. For three-digit numbers abc × 11, the answer is a, a+b, b+c, c, with carries handled identically.
This single trick saves about ten seconds on every multiplication-by-eleven question, of which there are typically two or three per paper. It is the lowest-effort, highest-yield Vedic technique a candidate can learn in five minutes. A similar pattern, with appropriate adjustments, works for multiplication by twelve, thirteen and other numbers slightly greater than ten.
Multiplication by Nine, Ninety-Nine and Powers of Nine
Multiplication by nine uses the simple identity n × 9 = n × 10 − n. For 47 × 9, compute 470 − 47 = 423. Multiplication by ninety-nine uses n × 99 = n × 100 − n. For 47 × 99, compute 4700 − 47 = 4653. Multiplication by 999 follows the same pattern. This method is faster than long multiplication for any factor in the nine-family and is particularly useful in time-and-work and percentage problems.
Multiplication by five uses n × 5 = n × 10 ÷ 2. For 86 × 5, compute 860 ÷ 2 = 430. Multiplication by twenty-five uses n × 25 = n × 100 ÷ 4. For 86 × 25, compute 8600 ÷ 4 = 2150. Multiplication by 125 uses n × 125 = n × 1000 ÷ 8. These three special cases together handle a large fraction of the calculations encountered in Banking and Staff Selection Commission papers, and each saves between five and fifteen seconds compared to long multiplication.
A Two-Week Mastery Plan for Multiplication
An efficient plan covers Vedic multiplication in two weeks. The first week dedicates two days to Nikhilam, two days to Urdhva-Tiryagbhyam, and three days to mixed practice combining both. The second week introduces the three special cases — multiplication by eleven, by nine and its powers, and by five and its powers — with one day each, followed by four days of mixed examination-style practice in which the candidate selects the correct technique for each question without prompting.
By the end of the fortnight, the candidate should be able to multiply any two two-digit numbers in under ten seconds and any two three-digit numbers in under twenty seconds with at least ninety-five-percent accuracy. This single skill alone saves three to five minutes in every Quantitative Aptitude paper, which translates directly into four to six additional attempted questions and five to ten additional marks — a return on investment unmatched by any other preparation activity in competitive examinations.