Why Speed Maths Matters
In competitive exams like SSC CGL, TSPSC Groups and Banking exams, you have less than 60 seconds per question on average. A student who can mentally calculate 45% of 360 in 5 seconds has a massive advantage over one who takes 30 seconds with pen-and-paper method.
Speed Maths — especially Vedic Mathematics techniques — can noticeably reduce your calculation time, because many multi-step calculations collapse into one mental step. Learning these tricks is one of the highest-return investments in your exam preparation, provided you practise them until they become automatic.
⚡ Simple maths of time: SSC CGL Tier-1 gives 60 minutes for 100 questions, i.e. 3600 s ÷ 100 = 36 seconds per question. Every second you save on calculation can be spent on questions that genuinely need thinking.
Trick 1: Multiplication by 11
Rule: Add the two digits and place the sum in the middle.
Example: 53 × 11 → 5 + 3 = 8 → Answer: 583
Example: 47 × 11 → 4 + 7 = 11 → write 1, carry 1 → Answer: 517
Practice this until it takes less than 3 seconds!
Trick 2: Squares of Numbers Ending in 5
Rule: Multiply the first digit by (first digit + 1), then write 25 at the end.
35² = 3 × 4 = 12 → Answer: 1225
75² = 7 × 8 = 56 → Answer: 5625
95² = 9 × 10 = 90 → Answer: 9025
Trick 3: Fast Percentage Calculation
Key principle: X% of Y = Y% of X
Use this when one percentage is easier to calculate than the other.
More shortcuts:
- 10% = divide by 10
- 5% = half of 10%
- 1% = divide by 100
- 15% = 10% + 5%
- 25% = divide by 4
- 33.33% ≈ divide by 3
Trick 4: Multiplication Near 100
Step 1: Difference from 100: 96→ -4, 97→ -3
Step 2: Left part: 96 - 3 = 93 (or 97 - 4 = 93)
Step 3: Right part: (-4) × (-3) = 12
Answer: 9312
Difference: +3 and +4. Left: 103+4 = 107. Right: 3×4 = 12. Answer: 10712
Trick 5: Divisibility Rules
| Divisible by | Rule | Example |
|---|---|---|
| 2 | Last digit is even | 348 ✓ |
| 3 | Sum of digits divisible by 3 | 123: 1+2+3=6 ✓ |
| 4 | Last 2 digits divisible by 4 | 1324: 24÷4=6 ✓ |
| 5 | Last digit is 0 or 5 | 375 ✓ |
| 6 | Divisible by both 2 and 3 | 132 ✓ |
| 8 | Last 3 digits divisible by 8 | 1000 ✓ |
| 9 | Sum of digits divisible by 9 | 729: 7+2+9=18 ✓ |
| 11 | (Sum of digits at odd places) − (Sum of digits at even places) = 0 or a multiple of 11 | 2728: (2+2) − (7+8) = −11 ✓ (2728 = 11 × 248) |
Trick 6: Approximation for Large Calculations
Most competitive exam questions allow approximation to ±1%. Round numbers smartly.
63² = 3969 exactly. Know squares up to 30 by heart: 16²=256, 17²=289, 18²=324...
Must memorize: Squares 1–30, Cubes 1–15, Square roots of perfect squares up to 400.
Trick 7: Ratio and Proportion Shortcuts
To find a value when ratios are given:
Total parts = 3+5 = 8. Value of 1 part = 80÷8 = 10. A = 3×10 = 30, B = 5×10 = 50.
This approach works for any ratio problem and takes under 15 seconds.
Trick 8: Compound Interest Shortcut
Or simply: CI = SI + (SI × r / 200)
Example: P=1000, r=10%, 2 years
SI = 200. Extra = 200×10/200 = 10. CI = 210
Once practised, this is quicker than substituting into the full compound-interest formula. It works only for 2 years.
Trick 9: Multiply by 5, 25, 125, 9 and 99
68 × 5 = 680 ÷ 2 = 340
44 × 25 = 4400 ÷ 4 = 1100
48 × 125 = 48000 ÷ 8 = 6000
37 × 9 = 370 − 37 = 333
46 × 99 = 4600 − 46 = 4554
Trick 10: Squares of Any Number — the (a+b)(a−b) Method
43²: d = 3 → (46 × 40) + 9 = 1840 + 9 = 1849
68²: d = 2 → (70 × 66) + 4 = 4620 + 4 = 4624
The idea comes from the identity (a+b)(a−b) = a² − b². Choose d so that one of the two factors ends in zero.
Trick 11: Successive Percentage Changes
Price rises 20%, then falls 10%: 20 − 10 + (20 × −10)/100 = 10 − 2 = +8%
Two discounts of 20% and 25%: −20 − 25 + (20 × 25)/100 = −45 + 5 = −40%, so the net discount is 40%.
Check with multipliers: 1.20 × 0.90 = 1.08 and 0.80 × 0.75 = 0.60 — the same answers.
Trick 12: Time, Speed, Work and Profit Formulas
Average speed for equal distances: 2xy / (x + y). For 30 km/h and 20 km/h: 2 × 30 × 20 / 50 = 24 km/h (not 25!).
Two people working together: (A × B) / (A + B) days. A = 10 days, B = 15 days → 150 / 25 = 6 days.
Same selling price, x% profit on one item and x% loss on the other: overall loss = x²/100 %. For x = 10 → 1% loss.
Boat and stream: downstream speed = boat + stream; upstream = boat − stream; boat speed = (down + up)/2.
Trick 13: Unit-Digit Cycles
| Base ends in | Cycle of last digit |
|---|---|
| 2 | 2, 4, 8, 6 |
| 3 | 3, 9, 7, 1 |
| 7 | 7, 9, 3, 1 |
| 8 | 8, 4, 2, 6 |
| 0, 1, 5, 6 | Always the same digit |
Unit digit of 7²³: the cycle length is 4 and 23 ÷ 4 leaves remainder 3, so take the 3rd digit of the cycle: 3 (check: 7³ = 343).
Which Trick Helps in Which Exam Topic?
| Exam topic | Use these tricks |
|---|---|
| Simplification / Approximation | Tricks 1, 2, 4, 9, 10 and the fraction–percentage table |
| Percentage, Profit & Loss, Discount | Tricks 3, 11, 12 |
| Time & Work, Time & Distance, Boats | Trick 12, Trick 7 |
| Interest | Trick 8 |
| Number System | Divisibility rules, Trick 13 |
Memory Tables You Must Know
Fraction-Percentage Equivalents
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/7 | 14.28% |
| 1/3 | 33.33% | 1/8 | 12.5% |
| 1/4 | 25% | 1/9 | 11.11% |
| 1/5 | 20% | 1/11 | 9.09% |
| 1/6 | 16.67% | 1/12 | 8.33% |
Daily Practice Plan for Speed Maths
- Warm-up (10 min): Mental multiplication of 2-digit numbers × single digit — do 20 problems daily
- Percentage practice (10 min): Calculate X% of Y for random values without a calculator
- Series completion (10 min): Number series — identify patterns quickly
- DI practice (20 min): Solve one full Data Interpretation set with a timer
- Mock test (30 min): Full Quantitative Aptitude section mock test with strict time limit
🎯 Goal: Practise daily for 30 days and track your own numbers: time taken for 20 mental problems on day 1 versus day 30, and your Quantitative Aptitude accuracy in mock tests. Your own trend tells you whether the routine works.
Practice Set — Try Before You Look at the Answers
Set a timer for 5 minutes and solve these nine questions mentally. Answers are listed below.
- 87 × 11
- 65²
- 98 × 97
- 36 × 25
- 15% of 240
- 24 × 99
- Net effect of two successive discounts of 20% and 25%
- Unit digit of 3⁴⁵
- Average speed if a person travels equal distances at 30 km/h and 20 km/h
Answers: 1) 957 2) 4225 3) 9506 4) 900 5) 36 6) 2376 7) 40% net discount 8) 3 9) 24 km/h
Common Mistakes While Using Shortcuts
- Learning many tricks, mastering none. Pick 5–6 tricks that match your weak topics and practise them daily instead of skimming 30.
- Using a trick where it does not apply. The "near 100" method needs both numbers close to 100; the "×11" method is for a single multiplier 11. Check the condition first.
- Skipping the tables. Tricks assume you know squares, cubes and basic tables instantly. Without them the shortcuts feel slow.
- Not checking the answer. Estimate the answer's size first (for example 96 × 97 must be a little under 10,000) so a slip in the last step is caught.
- Never practising under a timer. A trick is useful only if it is faster than your normal method at exam pressure. Test it in a mock test, not only on paper.
తెలుగులో సారాంశం (Summary in Telugu)
- Exam లో ఒక్కో ప్రశ్నకి సుమారు 36 సెకన్లు మాత్రమే ఉంటాయి (SSC CGL Tier-1: 60 నిమిషాలు, 100 ప్రశ్నలు).
- 11 తో గుణించడం: రెండు అంకెల మధ్యలో వాటి మొత్తాన్ని రాయండి (53 × 11 = 583).
- 5 తో ముగిసే సంఖ్య వర్గం: మొదటి అంకె × (దాని తర్వాతి సంఖ్య), చివర 25 (75² = 5625).
- 100 కి దగ్గరగా ఉన్న సంఖ్యల గుణకారం: 100 నుండి తేడాలు తీసి, వికర్ణంగా తీసివేసి, తేడాలను గుణించండి (98 × 97 = 9506).
- వరుస శాతం మార్పులు: x + y + xy/100 (20% పెరిగి 10% తగ్గితే నికరంగా +8%).
- సమాన దూరాలకు సగటు వేగం = 2xy/(x+y) (30 మరియు 20 → 24 km/h).
- రోజూ 30 నిమిషాలు practice చేసి, timer తో mock test లో పరీక్షించుకోండి.
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