Mental maths is the skill of calculating accurately without depending on a calculator, long rough work, or slow column methods. For SSC CGL, CHSL, CPO, Banking, Railways, CAT, NDA, CDS, and school exams, fast calculation is not just a talent. It is a repeatable system based on place value, complements, common fractions, tables, squares, cubes, and Vedic maths shortcuts.
This guide collects the most useful mental maths tricks for addition, subtraction, multiplication, division, percentages, successive percentages, squares, cubes, square roots, cube roots, prime numbers, HCF, LCM, and approximation. After each major topic, you will also find links to InspectorsPrep practice tools so you can immediately train the trick under a timer.
Quick Answer: How to Improve Mental Maths Speed?
To improve mental maths speed, train in this order: left-to-right addition, base subtraction, multiplication tables, squares up to 30, cubes up to 20, fraction-to-percentage values, Vedic multiplication near 100, successive percentage formula, HCF LCM factorization, and timed mixed arithmetic drills. Daily 15-minute practice is enough if every session is timed and accuracy-tracked.
1. Why Mental Maths Matters in SSC and Banking Exams
In SSC and Banking exams, most candidates lose time not because the concept is impossible, but because the arithmetic becomes slow. A profit and loss question may need percentage conversion. A data interpretation set may require addition, subtraction, multiplication, average, and ratio calculation in one chain. If each small calculation takes 20 seconds, the full question becomes unmanageable.
Mental maths tricks reduce calculation friction. They help you estimate options, eliminate wrong answers, verify DI totals, and maintain speed in high-pressure sections. For Bank PO and Clerk exams, fast approximation is essential in simplification, number series, quadratic comparison, and DI. For SSC CGL and CHSL, arithmetic topics such as percentage, ratio, SI CI, profit and loss, time and work, speed distance time, and mensuration all become easier when calculation speed is strong.
| Exam Area | Where Mental Maths Helps | Best Tricks to Use |
|---|---|---|
| Data Interpretation | Tables, charts, averages, percentage change | Left-to-right addition, approximation, percentage fractions |
| Arithmetic | Profit loss, SI CI, time work, partnership | Successive percentages, multiplication shortcuts, fraction values |
| Number System | Factors, divisibility, LCM, HCF | Prime factorization, divisibility tests, difference method |
| Simplification | BODMAS, roots, powers, decimal operations | Squares, cubes, square roots, cube roots, decimal shifting |
2. Addition Tricks
Left-to-Right Addition Method
Add numbers in the same direction you read them. Instead of starting from the units place, combine larger place values first. For 76 + 58, think 70 + 50 = 120, then 6 + 8 = 14, so the final answer is 134.
Split-Add Method for Large Numbers
Keep the first number whole and split only the second number. For 456 + 287, think 456 + 200 = 656, then +80 = 736, then +7 = 743. This protects working memory because only one running total changes.
Complement Addition Trick
Round messy numbers to a clean base, then adjust. For 397 + 256, treat 397 as 400 - 3. Now 400 + 256 = 656, and 656 - 3 = 653.
Pairing to 10, 100, and 1000
When adding a string, pair friendly numbers first: 47 + 18 + 53 + 82 becomes (47 + 53) + (18 + 82) = 100 + 100 = 200. This is extremely useful in DI table addition.
3. Subtraction Tricks
Compensation Method
Subtract a nearby easy number, then adjust. For 1000 - 487, subtract 500 first to get 500. Since 487 is 13 less than 500, add 13 back. Answer: 513.
Subtract From Base Trick
For numbers like 10000 - 6742, subtract every digit from 9 except the last digit from 10. So 9 - 6 = 3, 9 - 7 = 2, 9 - 4 = 5, and 10 - 2 = 8. Answer: 3258.
Difference by Counting Up
For 823 - 568, ask how much must be added to 568 to reach 823. 568 + 32 = 600, +200 = 800, +23 = 823. Total difference is 32 + 200 + 23 = 255.
Equal Addition Method
Add the same number to both values to make the subtraction easier. For 734 - 298, add 2 to both numbers: 736 - 300 = 436. The difference remains unchanged.
4. Multiplication Tricks
Multiply by 11
For a two-digit number, add the two digits and place the sum between them. 53 x 11 = 583 because 5 + 3 = 8. If the middle sum is two digits, carry the tens digit: 78 x 11 = 858 because 7 + 8 = 15, write 5 and carry 1 to 7.
Multiply by 5, 25, and 125
- Multiply by 5: multiply by 10 and divide by 2. Example: 48 x 5 = 240.
- Multiply by 25: multiply by 100 and divide by 4. Example: 64 x 25 = 1600.
- Multiply by 125: multiply by 1000 and divide by 8. Example: 56 x 125 = 7000.
Nikhilam Method: Multiplication Near 100
For 98 x 97, use base 100. Deficiencies are -2 and -3. Cross subtract: 98 - 3 = 95. Multiply deficiencies: 2 x 3 = 06. Answer: 9506.
Multiplication Near 1000
For 997 x 992, base is 1000. Deficiencies are -3 and -8. Cross subtract: 997 - 8 = 989. Deficiency product: 3 x 8 = 024 because the base has three zeroes. Answer: 989024.
Urdhva Tiryagbhyam: Vertical and Crosswise
For 23 x 14: units 3 x 4 = 12, write 2 carry 1. Crosswise: 2 x 4 + 3 x 1 = 11, plus carry 1 = 12, write 2 carry 1. Tens: 2 x 1 = 2, plus carry 1 = 3. Answer: 322.
Multiply by 99, 999, and 9999
Multiply by the next power of 10 and subtract the number once. 46 x 99 = 46 x (100 - 1) = 4600 - 46 = 4554.
5. Division Tricks
Divide by 5, 25, and 125
- Divide by 5: multiply by 2 and divide by 10. Example: 245 / 5 = 490 / 10 = 49.
- Divide by 25: multiply by 4 and divide by 100. Example: 725 / 25 = 2900 / 100 = 29.
- Divide by 125: multiply by 8 and divide by 1000. Example: 3750 / 125 = 30000 / 1000 = 30.
Divisibility Tests
| Divisor | Quick Test | Example |
|---|---|---|
| 2 | Last digit is even | 748 is divisible by 2 |
| 3 | Digit sum is divisible by 3 | 348: 3 + 4 + 8 = 15 |
| 4 | Last two digits divisible by 4 | 2316 because 16 is divisible by 4 |
| 8 | Last three digits divisible by 8 | 4312 because 312 is divisible by 8 |
| 9 | Digit sum is divisible by 9 | 729: 7 + 2 + 9 = 18 |
| 11 | Difference between alternate digit sums is 0 or multiple of 11 | 121: (1 + 1) - 2 = 0 |
6. Percentage Tricks
Find 10%, 5%, 1%, and 50%
Move the decimal one place left for 10%. Half of 10% gives 5%. Move the decimal two places left for 1%. Half the number for 50%. Example: for 640, 10% = 64, 5% = 32, 1% = 6.4, and 50% = 320.
Use Fraction Equivalents
| Percentage | Fraction | Use Case |
|---|---|---|
| 50% | 1/2 | Half the value |
| 33.33% | 1/3 | Divide by 3 |
| 25% | 1/4 | Divide by 4 |
| 20% | 1/5 | Divide by 5 |
| 16.66% | 1/6 | Divide by 6 |
| 12.5% | 1/8 | Divide by 8 |
| 11.11% | 1/9 | Divide by 9 |
| 8.33% | 1/12 | Divide by 12 |
| 6.25% | 1/16 | Divide by 16 |
Percentage Increase and Decrease
Increase 240 by 20%: 20% of 240 = 48, so final value = 288. Decrease 800 by 12.5%: 12.5% is 1/8, so 800 - 100 = 700.
7. Successive Percentage Tricks
For two successive percentage changes, use a + b + ab/100. Treat increase as positive and decrease as negative.
Two Increases
Increase by 20% and then 30%: 20 + 30 + (20 x 30)/100 = 56%. Net increase is 56%.
Increase Then Decrease
Increase by 20% and then decrease by 20%: 20 - 20 + (20 x -20)/100 = -4%. The final value is 4% less, not equal to the original.
Price and Consumption Trick
If price increases by x%, consumption must decrease by x / (100 + x) x 100 percent to keep expenditure constant. If price rises 25%, required consumption decrease is 25/125 x 100 = 20%.
8. Square Tricks
Numbers Ending in 5
For n5 squared, multiply n by n + 1 and append 25. Example: 35 square = 3 x 4 followed by 25 = 1225.
Square Near 100
For 96 square, deficiency from 100 is 4. Left part: 96 - 4 = 92. Right part: 4 square = 16. Answer: 9216.
Square Near 50
Use 50 as base. For 47 square, write 25 - 3 = 22 as the first part and 3 square = 09 as the second part. Answer: 2209. For 53 square, write 25 + 3 = 28 and 3 square = 09. Answer: 2809.
General Algebra Method
Use (a + b)^2 = a^2 + 2ab + b^2. For 104 square, 10000 + 800 + 16 = 10816.
9. Cube Tricks
Memorize cubes from 1 to 20 because they appear repeatedly in simplification and root questions. The most important values are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, and 8000.
Cube Near Base
Use (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. For 102 cube, take a = 100 and b = 2. Answer = 1000000 + 60000 + 1200 + 8 = 1061208.
Cube Ending Pattern
The last digit of a cube depends on the last digit of the number. Numbers ending in 2 cube to last digit 8; ending in 3 cube to 7; ending in 7 cube to 3; ending in 8 cube to 2. This pattern is essential for cube root shortcuts.
10. Square Root Tricks
For perfect square roots, split the number into pairs from the right. The last pair gives the possible last digit, and the remaining left part helps identify the tens digit.
Example: Square Root of 1764
The last digit is 4, so the root ends in 2 or 8. The first part is 17. Since 4 square = 16 and 5 square = 25, the tens digit is 4. Now compare with 45 square = 2025. Since 1764 is less than 2025, choose the smaller ending: 42. So square root of 1764 is 42.
Perfect Square Ending Clues
A perfect square cannot end in 2, 3, 7, or 8. If the unit digit is 1, root ends in 1 or 9. If it is 4, root ends in 2 or 8. If it is 6, root ends in 4 or 6. If it is 9, root ends in 3 or 7.
11. Cube Root Tricks
For cube roots of perfect cubes, separate the last three digits. The last digit gives the unit digit of the answer, and the remaining part gives the tens digit.
Example: Cube Root of 17576
The last digit is 6, so the cube root ends in 6. Remove the last three digits: 17 remains. Since 2 cube = 8 and 3 cube = 27, the tens digit is 2. Answer: 26.
Cube Root Unit Digit Map
| Cube Last Digit | Root Last Digit |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 8 |
| 3 | 7 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 3 |
| 8 | 2 |
| 9 | 9 |
12. Prime Number Tricks
A prime number has exactly two factors: 1 and itself. To test whether a number is prime, check divisibility only up to its square root. For example, to test 97, you only need to check primes up to 9.8: 2, 3, 5, and 7. It is not divisible by any of these, so 97 is prime.
Prime Check Shortcut
- Reject even numbers greater than 2.
- Reject numbers ending in 5 or 0 greater than 5.
- Check digit sum for divisibility by 3.
- Check 7 only when needed for two-digit and three-digit numbers.
Common Primes to Memorize
Memorize primes up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
13. HCF and LCM Tricks
Prime Factorization Method
For HCF of 24 and 36, write 24 = 2 x 2 x 2 x 3 and 36 = 2 x 2 x 3 x 3. Common factors are 2 x 2 x 3 = 12. So HCF is 12.
LCM x HCF Formula
For two numbers, LCM x HCF = product of the numbers. If numbers are 12 and 18, product = 216 and HCF = 6. So LCM = 216 / 6 = 36.
Difference Method for HCF
The HCF of two numbers must divide their difference. For 84 and 126, the difference is 42. Since 42 divides both numbers, HCF is 42. This method is very fast in number system questions.
Co-prime LCM Shortcut
If two numbers have no common factor except 1, their LCM is their product. Example: LCM of 8 and 15 is 120 because they are co-prime.
14. Vedic Maths Tricks to Know
| Vedic Method | Meaning | Best Use |
|---|---|---|
| Nikhilam Navatashcaramam Dashatah | All from 9 and last from 10 | Multiplication and subtraction near 10, 100, 1000 |
| Urdhva Tiryagbhyam | Vertically and crosswise | Fast multiplication of two-digit and three-digit numbers |
| Ekadhikena Purvena | By one more than the previous one | Squaring numbers ending in 5 |
| Anurupyena | Proportionately | Multiplication near working bases like 50, 200, 500 |
| Paravartya Yojayet | Transpose and apply | Division patterns and algebraic simplification |
| Yavadunam | Whatever the deficiency | Squaring numbers near base values |
Do not try to memorize Vedic sutras as Sanskrit phrases only. Learn the calculation pattern behind them. In exams, the result matters: clean bases, fast cross-multiplication, complements, and fewer written steps.
15. Recommended Mental Maths Practice Tools
After reading a trick, practice it immediately. Fast calculation becomes automatic only when your brain repeats the same pattern under a timer.
You can also visit the main Mental Calculation Engine and the InspectorsPrep Dashboard to organize daily practice.
16. Daily Mental Maths Practice Routine
Use a 15-minute daily routine. Spend 5 minutes on addition and subtraction, 5 minutes on multiplication tables and percentages, and 5 minutes on squares, cubes, roots, HCF, LCM, and mixed arithmetic. Keep your accuracy above 90% before increasing speed.
- Warm up with complements of 10, 100, and 1000.
- Do one timed addition or subtraction round.
- Revise tables from 12 to 30, squares up to 30, and cubes up to 20.
- Practice 10 percentage conversions from fractions.
- Finish with one mixed mental arithmetic drill.
Frequently Asked Questions
What are mental maths tricks?
Mental maths tricks are shortcuts used to solve arithmetic without calculators or long written steps. They use place value, complements, Vedic maths methods, tables, squares, cubes, divisibility, and fraction patterns.
How can I improve mental maths speed?
Practice timed drills daily. Start with basic addition and subtraction, then add multiplication, percentages, squares, cubes, roots, and HCF LCM. Speed improves when the same patterns are repeated under time pressure.
Which mental maths tricks are best for SSC CGL?
The best SSC CGL tricks are left-to-right addition, base subtraction, percentage fractions, successive percentage formula, Vedic multiplication near base values, squares ending in 5, square root shortcuts, cube root shortcuts, and HCF LCM factorization.
Are Vedic maths tricks useful for Bank PO and Clerk exams?
Yes. Banking exams require fast simplification, approximation, DI, percentage calculation, and arithmetic. Vedic maths tricks help reduce rough work and improve option elimination speed.
How many days are needed to improve calculation speed?
Most students notice improvement within 15 to 30 days if they practice for 15 minutes daily with a timer and track accuracy. The key is consistency, not long irregular sessions.
Should students memorize squares and cubes?
Yes. Memorize squares up to 30 and cubes up to 20. This single habit saves time in simplification, roots, mensuration, number system, and approximation questions.
Written by: Founder
Founder of InspectorsPrep.in, full-stack data architect and currently working in the Income Tax Department. These mental maths guides and practice tools are built for SSC, Banking, and competitive exam aspirants who want faster arithmetic with higher accuracy.