Introduction
Vedic Mathematics is a powerful system of mathematical shortcuts derived from ancient Indian mathematical principles. It helps students perform calculations quickly and accurately without relying heavily on calculators. These techniques are widely used in competitive exams such as SSC, Banking, NDA, CDS, CAT, Railway, UPSC, and other aptitude tests.
In this series, we will cover 100 Vedic Maths Tricks with their names, formulas, explanations, and solved examples.
This is Part 1, covering Tricks 1 to 25.
Trick 1: Ekadhikena Purvena – Square Numbers Ending in 5
Meaning
“By one more than the previous one.”
Formula
If a number ends in 5:
n5² = n × (n + 1) followed by 25
Example
25²
2 × 3 = 6
Answer = 625
Practice
45² = 2025
75² = 5625
Trick 2: Ekadhikena Purvena – 35² Shortcut
Formula
3 × 4 = 12
Append 25
Example
35² = 1225
Practice
55² = 3025
65² = 4225
Trick 3: Ekadhikena Purvena – 85² Shortcut
Example
85²
8 × 9 = 72
Append 25
Answer = 7225
Practice
95² = 9025
Trick 4: Nikhilam Sutra – Multiplication Near 100
Meaning
“All from 9 and the last from 10.”
Example
97 × 96
Deficiencies:
97 = -3
96 = -4
97 – 4 = 93
3 × 4 = 12
Answer = 9312
Trick 5: Nikhilam – 98 × 97
98 = -2
97 = -3
98 – 3 = 95
2 × 3 = 06
Answer = 9506
Trick 6: Nikhilam – 99 × 98
99 = -1
98 = -2
99 – 2 = 97
1 × 2 = 02
Answer = 9702
Trick 7: Nikhilam – Numbers Near 1000
Example
998 × 997
998 – 3 = 995
2 × 3 = 006
Answer = 995006
Trick 8: Nikhilam – 999 × 998
999 – 2 = 997
1 × 2 = 002
Answer = 997002
Trick 9: Urdhva-Tiryagbhyam – Vertical and Crosswise Multiplication
Example
12 × 13
Vertical:
1 × 1 = 1
Crosswise:
(1 × 3) + (2 × 1) = 5
Vertical:
2 × 3 = 6
Answer = 156
Trick 10: Urdhva-Tiryagbhyam – 23 × 14
2 × 1 = 2
(2 × 4) + (3 × 1) = 11
3 × 4 = 12
Answer = 322
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Trick 11: Same First Digit Trick
Formula
When first digits are same and last digits total 10.
Example
43 × 47
4 × 5 = 20
3 × 7 = 21
Answer = 2021
Trick 12: Same First Digit Trick
Example
62 × 68
6 × 7 = 42
2 × 8 = 16
Answer = 4216
Trick 13: Same First Digit Trick
Example
84 × 86
8 × 9 = 72
4 × 6 = 24
Answer = 7224
Trick 14: Multiply by 11
Formula
Add neighboring digits.
Example
23 × 11
2 + 3 = 5
Answer = 253
Trick 15: Multiply by 11
Example
54 × 11
5 + 4 = 9
Answer = 594
Trick 16: Multiply by 5
Formula
Divide by 2 and multiply by 10.
Example
48 × 5
48 ÷ 2 = 24
Answer = 240
Trick 17: Multiply by 25
Formula
Divide by 4 and add two zeros.
Example
64 × 25
64 ÷ 4 = 16
Answer = 1600
Trick 18: Multiply by 125
Formula
Divide by 8 and add three zeros.
Example
48 × 125
48 ÷ 8 = 6
Answer = 6000
Trick 19: Multiply by 50
Formula
Multiply by 5 and append zero.
Example
34 × 50
34 × 5 = 170
Answer = 1700
Trick 20: Multiply by 15
Formula
Multiply by 10 and add half.
Example
20 × 15
20 × 10 = 200
Half of 200 = 100
Answer = 300
Trick 21: Multiply by 12
Formula
Multiply by 10 and add twice the number.
Example
25 × 12
250 + 50
Answer = 300
Trick 22: Multiply by 99
Formula
Multiply by 100 and subtract the number.
Example
47 × 99
4700 – 47
Answer = 4653
Trick 23: Multiply by 999
Formula
Multiply by 1000 and subtract the number.
Example
123 × 999
123000 – 123
Answer = 122877
Trick 24: Double-Half Method
Example
16 × 25
8 × 50
4 × 100
Answer = 400
Why it Works
One number is halved while the other is doubled.
Trick 25: Consecutive Number Multiplication
Formula
n × (n + 1)
Example
12 × 13
12² + 12
144 + 12
Answer = 156
Practice
14 × 15
196 + 14
Answer = 210
Summary of Tricks Covered
Ekadhikena Purvena
- Tricks 1–3
Nikhilam Sutra
- Tricks 4–8
Urdhva-Tiryagbhyam
- Tricks 9–10
Same First Digit Multiplication
- Tricks 11–13
Quick Multiplication Methods
- Tricks 14–25
These 25 tricks form the foundation of Vedic Mathematics and are among the most frequently used shortcuts in competitive examinations and mental arithmetic.