Arithmetic Shortcuts & Tricks - Complete SSC CGL Guide
What are Arithmetic Shortcuts? These are smart calculation techniques that help solve complex arithmetic problems in seconds instead of minutes. Mastering these can save 50-70% calculation time in SSC CGL, giving you a massive competitive edge.
Traditional Method
Step-by-step calculation
Shortcut Method
Direct answer in 1-2 steps
70% Time Saved Per Question!
Pro Tip – Master These 3 Categories First!
1. Percentage Tricks (Most frequent in SSC)
2. Multiplication Shortcuts (Saves maximum time)
3. Vedic Sutras (For complex calculations)
Visit SKY Practice for 1000+ shortcut practice questions with instant feedback.
Smart calculations can reduce solving time from minutes to seconds
1. Vedic Mathematics
What is Vedic Math? Ancient Indian system of mathematics based on 16 sutras (formulas) that make calculations 10-15 times faster.
Essential Vedic Sutras for SSC
Why Vedic Math for SSC?
Vedic Math techniques work like magic for SSC calculations. They eliminate lengthy steps and provide answers directly. Focus on these 5 key sutras.
Ekadhikena Purvena
"By one more than the previous one"
Example: 25² = (2×3)|25 = 625
75² = (7×8)|25 = 5625
115² = (11×12)|25 = 13225
Nikhilam Navatashcaramam
"All from 9, last from 10"
Base 100: 98×97
98: -2, 97: -3
Answer: (98-3)|(2×3)
= 95|06 = 9506
Urdhva-Tiryagbhyam
"Vertically and crosswise"
12×13: (1×1)|(1×3+2×1)|(2×3)
= 1|5|6 = 156
23×24: (2×2)|(2×4+3×2)|(3×4)
= 4|14|12 = 4|15|2 = 552
Vedic Math Application Examples
5×45=225
Total=2025
Time saved: 30 seconds → 5 seconds!
SSC Shortcut: Must-Know Vedic Formulas
Square numbers ending in 5: n5² = n×(n+1)|25
Multiply by 11: 24×11 = 2|(2+4)|4 = 264
Multiply by 99: 46×99 = 4600-46 = 4554
Multiply by 5: ×5 = ×10÷2
Multiply by 25: ×25 = ×100÷4
Solved Example: Vedic Multiplication
Both numbers near 100
104 = 100+4
106 = 100+6
Step 2: Apply formula
For numbers above base:
Answer = (104+6) | (4×6)
= 110 | 24
Step 3: Adjust for base
Since base is 100, left part = 110 means 11000
So answer = 11000 + 24 = 11024
Step 4: Verification
104 × 106 = (100+4)(100+6)
= 10000 + 600 + 400 + 24
= 10000 + 1000 + 24 = 11024 ✓
Alternative: Cross-check
104 × 100 = 10400
104 × 6 = 624
Total = 10400 + 624 = 11024 ✓
Final Answer: 11024
2. Percentage Tricks
Why Important? Percentage questions appear in every SSC paper. Mastering these tricks can save 1-2 minutes per question.
Percentage Calculation Shortcuts
Fraction-Percentage Equivalents
Memorize these common conversions. They eliminate division and multiplication in percentage calculations.
SSC Shortcut: Percentage Calculations
10%: Move decimal one place left: 10% of 450 = 45
5%: Half of 10%: 5% of 450 = 22.5
20%: Double of 10%: 20% of 450 = 90
15%: 10% + 5%: 15% of 450 = 45 + 22.5 = 67.5
25%: Divide by 4: 25% of 440 = 110
33.33%: Divide by 3: 33.33% of 900 = 300
Percentage Increase/Decrease
Final = Original × (1 ± p₁/100) × (1 ± p₂/100)
Quick formula for two changes:
Net % = p₁ + p₂ + (p₁×p₂)/100
= 5 - 3 = 2% increase
Percentage of Percentage
Example:
20% of 30% = (20×30)/100 %
= 600/100 % = 6%
10% of 800 = 80
Base Value Problems
y = (x × 100)/p
If x is p% more than y, then
y = x/(1 + p/100)
If x is p% less than y, then
y = x/(1 - p/100)
Solved Example: Percentage Tricks
Let number = 100
After 20% increase = 100 + 20 = 120
After 20% decrease = 120 - 20% of 120
= 120 - 24 = 96
Net change = 96 - 100 = -4
Percentage = (-4/100)×100 = -4%
Shortcut method:
Use formula: Net % = p + q + (p×q)/100
Here p = +20%, q = -20%
Net % = 20 - 20 + (20×-20)/100
= 0 - 400/100 = -4%
Ultra-short method:
For equal % increase and decrease:
Net % = -(p²/100)
= -(20²/100) = -400/100 = -4%
Verification with different number:
Let number = 200
Increase: 200 + 40 = 240
Decrease: 240 - 48 = 192
Change: 192-200 = -8 (4% of 200) ✓
Final Answer: 4% decrease
Mastering shortcuts can transform 2-minute calculations into 10-second solutions
3. Multiplication Shortcuts
Time Savers: Multiplication is the most frequent operation in SSC. These tricks can reduce calculation time by 80%.
Lightning Multiplication Techniques
The Power of Decomposition
Break numbers into easier parts, multiply, then combine. Works for all multiplication problems.
Multiply by 5, 25, 125
×25 = ×100 ÷ 4
×125 = ×1000 ÷ 8
Example: 48×125
= 48×1000 ÷ 8
= 48000 ÷ 8 = 6000
Multiply by 11, 111
23×11 = 2|(2+3)|3 = 253
×111: Write first digit, sum of first two, sum of all three, sum of last two, last digit
23×111 = 2553
Multiply by 9, 99, 999
×99 = ×100 - number
×999 = ×1000 - number
68×99 = 6800 - 68 = 6732
123×999 = 123000 - 123 = 122877
SSC Shortcut: Special Multiplications
Multiply numbers close to 100: 98×103 = (98+3)|(2×3) = 101|06 = 10106
Multiply by 15: ×15 = ×10 + half of ×10 = ×10 + ×5
Multiply by 75: ×75 = ×100 × 3/4
Multiply by 125: ×125 = ×1000 ÷ 8
Multiply two 2-digit numbers: Cross multiplication method
Time Comparison: 48 × 125
80% Time Saved!
Solved Example: Complex Multiplication
47 × 53 = (50-3) × (50+3)
= 50² - 3² = 2500 - 9 = 2491
Method 2: Base method (both near 50)
47: -3 from 50
53: +3 from 50
Answer = (47+3) or (53-3) | (3×3)
= 50 | 09 = 2500 - 9? Wait, need adjustment
Actually: (Base = 50, so multiply left part by 50)
= (50 × 50) + (3×3) with sign? Let's do properly:
Method 3: Nikhilam (Base 100)
47: -53 from 100? Too far. Better use method 1.
Method 4: Direct multiplication shortcut
47 × 50 = 2350
47 × 3 = 141
Total = 2350 + 141 = 2491
Method 1 is fastest:
50² = 2500 (instant)
3² = 9 (instant)
2500 - 9 = 2491 (instant)
Verification:
47 × 53:
40×53 = 2120
7×53 = 371
Total = 2120+371 = 2491 ✓
Final Answer: 2491 (using difference of squares in 3 seconds)
4. Division Tricks
Simplify Division: Division can be converted to multiplication or handled through simplification tricks.
Smart Division Techniques
Converting Division to Multiplication
Dividing by 5, 25, 125 etc. is easier when converted to multiplication by 2, 4, 8 etc.
Divide by 5, 25, 125
÷25 = ×4 ÷ 100
÷125 = ×8 ÷ 1000
Example: 375 ÷ 125
= 375 × 8 ÷ 1000
= 3000 ÷ 1000 = 3
Divisibility Rules
- 2: Last digit even
- 3: Sum of digits divisible by 3
- 4: Last 2 digits divisible by 4
- 5: Last digit 0 or 5
- 6: Divisible by 2 and 3
- 8: Last 3 digits divisible by 8
- 9: Sum of digits divisible by 9
- 11: Difference of alternate sums
Division by Fractions
Example: 48 ÷ (3/4)
= 48 × (4/3)
= (48/3) × 4
= 16 × 4 = 64
SSC Shortcut: Quick Division
Divide by 5: ×2, move decimal left: 48÷5 = 9.6
Divide by 25: ×4, move decimal left twice: 75÷25 = 3
Divide by 125: ×8, move decimal left thrice: 250÷125 = 2
Divide by 9: Sum of digits (recurring): 1/9 = 0.111..., 2/9 = 0.222...
Divide by 11: 1/11 = 0.0909..., 2/11 = 0.1818...
Solved Example: Division Shortcut
25 × 10 = 250
25 × 5 = 125
Total: 250+125 = 375
So 10+5 = 15
Shortcut method 1:
÷25 = ×4 ÷ 100
375 × 4 = 1500
1500 ÷ 100 = 15
Shortcut method 2:
375 ÷ 100 = 3.75
3.75 × 4 = 15
Shortcut method 3:
For ÷25: Divide by 100, multiply by 4
Or: Divide by 5, then divide by 5 again
375 ÷ 5 = 75
75 ÷ 5 = 15
Ultra-short method:
25×4 = 100
So (375×4)÷100 = 1500÷100 = 15
Time comparison:
Traditional: 15-20 seconds
Shortcut: 3-5 seconds
Final Answer: 15
5. Approximation Techniques
Exam Strategy: In SSC, exact calculation isn't always needed. Approximation can give answers within 1-2% error in 1/4th time.
Smart Approximation Rules
When to Use Approximation
1. Options are far apart (10%+ difference)
2. Complex calculations with decimals
3. Time is running out
4. Verification of exact answer
Rounding Rules
- Nearest 10: 47 ≈ 50, 43 ≈ 40
- Nearest 100: 247 ≈ 250, 243 ≈ 240
- For multiplication: Round one up, one down
- For division: Round both in same direction
- Keep track: Note if rounding up or down
- Error check: Estimate error percentage
Decimal Approximation
1/6 ≈ 0.167 (actual 0.1666...)
1/7 ≈ 0.143 (actual 0.142857...)
1/9 ≈ 0.111 (actual 0.111...)
1/11 ≈ 0.091 (actual 0.0909...)
1/12 ≈ 0.083 (actual 0.0833...)
√2 ≈ 1.414, √3 ≈ 1.732
π ≈ 3.14 or 22/7
Percentage Approximation
33.33% ≈ 33.3% or 1/3
66.67% ≈ 66.7% or 2/3
11.11% ≈ 11.1% or 1/9
9.09% ≈ 9.1% or 1/11
8.33% ≈ 8.3% or 1/12
For quick calc: 1% = 1/100
SSC Shortcut: Approximation Guidelines
Multiplication: 47×53 ≈ 50×50 = 2500 (actual 2491, error 0.36%)
Division: 149÷7 ≈ 150÷7 ≈ 21.43 (actual 21.2857, error 0.68%)
Percentage: 33.33% of 897 ≈ 1/3 of 900 = 300 (actual 299, error 0.33%)
Square root: √50 ≈ 7.07 (between 7²=49 and 7.1²=50.41)
When NOT to approximate: Options are close (1-2% difference)
Solved Example: Approximation
149 × 151 = 22499
22499 ÷ 75 = 299.9866...
Approximation method 1:
149 ≈ 150, 151 ≈ 150, 75 exact
150 × 150 = 22500
22500 ÷ 75 = 300
Error = 0.0133/300 × 100 = 0.0044% (negligible)
Approximation method 2 (Vedic):
149 × 151 = (150-1)(150+1) = 150² - 1² = 22500 - 1 = 22499
22499 ÷ 75 = (22500-1)/75 = 300 - 1/75 = 300 - 0.0133 = 299.9867
Approximation method 3 (percentage):
149 × 151 ÷ 75 = 149 × (151/75)
151/75 ≈ 2.0133
149 × 2.0133 ≈ 150 × 2.0133 - 1 × 2.0133
≈ 301.995 - 2.0133 = 299.9817
Quickest approximation:
149 ≈ 150, 151 ≈ 150, 150×150=22500
22500 ÷ 75 = 22500 × 4/300 = 90000/300 = 300
Time comparison:
Exact: 30-40 seconds
Approximation: 5-10 seconds
Final Answer: Approximately 300
6. Square & Cube Shortcuts
Instant Squares: Learn to calculate squares and cubes mentally without multiplication.
Square & Cube Formulas
Algebraic Identities for Squares
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
a² - b² = (a+b)(a-b)
These make squaring much faster.
Squares of Numbers Ending in 5
Examples:
15²: 1×2=2|25=225
25²: 2×3=6|25=625
35²: 3×4=12|25=1225
45²: 4×5=20|25=2025
105²: 10×11=110|25=11025
Squares Near 50, 100
48² = 2500 - 200 + 4 = 2304
53² = 2500 + 300 + 9 = 2809
Near 100: (100±d)² = 10000 ± 200d + d²
98² = 10000 - 400 + 4 = 9604
Cube Shortcuts
11³ = 1331 (1|3|3|1 pattern)
12³ = 1728
13³ = 2197
Memorize: 1-10 cubes
1³=1, 2³=8, 3³=27, 4³=64, 5³=125
6³=216, 7³=343, 8³=512, 9³=729, 10³=1000
SSC Shortcut: Square Roots
Perfect squares to know: 1-30 squares (especially 11²=121 to 25²=625)
√ ending in 25: √625 = 25, √1225 = 35, √2025 = 45
Estimation: √50 ≈ 7.07, √75 ≈ 8.66, √90 ≈ 9.49
Quick method: √x ≈ average of a and x/a where a² close to x
Example: √80 ≈ average of 8 and 10 = 9 (actual 8.944)
Solved Example: Square Calculation
46 = 50 - 4
46² = (50-4)² = 50² - 2×50×4 + 4²
= 2500 - 400 + 16 = 2116
Method 2: Using base 50
For numbers near 50: (50-d)² = (25-d)|d²
But d² should be 2-digit, so adjust
Actually: (50-d)² = 2500 - 100d + d²
46 = 50-4, d=4
2500 - 400 + 16 = 2116
Method 3: Using (a+b)(a-b)
46² = (46+4)(46-4) + 4²
= 50×42 + 16 = 2100 + 16 = 2116
Method 4: Direct multiplication shortcut
40² = 1600
2×40×6 = 480
6² = 36
Total = 1600+480+36 = 2116
Fastest method: Method 1 or 3
Time: 5-7 seconds vs traditional 20-25 seconds
Verification:
46 × 40 = 1840
46 × 6 = 276
Total = 1840+276 = 2116 ✓
Final Answer: 2116
7. Time-Speed-Distance Shortcuts
TSD Formulas: These problems appear in every SSC exam. Shortcuts can solve them in 15-20 seconds.
TSD Formula Shortcuts
Basic Relationships
Distance = Speed × Time
Speed = Distance / Time
Time = Distance / Speed
Always ensure units are consistent.
Average Speed
Avg speed = 2v₁v₂/(v₁+v₂)
Different distances: d₁ at v₁, d₂ at v₂
Avg speed = (d₁+d₂)/(t₁+t₂)
= (d₁+d₂)/(d₁/v₁ + d₂/v₂)
Relative Speed
Opposite direction: v₁ + v₂
Time to meet = Distance/(v₁ ± v₂)
Trains passing:
Time = (L₁+L₂)/(v₁ ± v₂)
Boats & Streams
Upstream: b - s
Boat speed = (d+u)/2
Stream speed = (d-u)/2
d = downstream speed
u = upstream speed
SSC Shortcut: TSD Conversions
km/h to m/s: ×5/18 (or ÷3.6)
m/s to km/h: ×18/5 (or ×3.6)
Example: 72 km/h = 72×5/18 = 20 m/s
Time: 2.5 hours = 2h 30min = 150 minutes
Distance: When speeds in ratio, distances in same ratio if time same
Meeting problems: Use concept of relative distance covered
Solved Example: TSD Shortcut
Let total distance = 2d
Time for first half = d/40
Time for second half = d/60
Total time = d/40 + d/60 = d(1/40+1/60) = d(3/120+2/120) = 5d/120 = d/24
Average speed = total distance/total time = 2d/(d/24) = 48 km/h
Shortcut method 1:
When equal distances: Avg speed = 2v₁v₂/(v₁+v₂)
= 2×40×60/(40+60) = 4800/100 = 48 km/h
Shortcut method 2 (assume distance):
Assume distance = 120 km (LCM of 40,60)
First half (60 km) at 40 km/h: time = 60/40 = 1.5h
Second half (60 km) at 60 km/h: time = 60/60 = 1h
Total time = 2.5h, Total distance = 120 km
Average = 120/2.5 = 48 km/h
Shortcut method 3 (ratio):
Time ratio: t₁:t₂ = (1/40):(1/60) = 3:2
Let total time = 5 units
Distance = 40×3 + 60×2 = 120+120 = 240 units? Wait
Actually: Distance covered in 3 units at 40 = 120
Distance in 2 units at 60 = 120
Total distance = 240 in 5 units time
Speed = 240/5 = 48 km/h
Time comparison:
Traditional: 30-40 seconds
Shortcut: 5-10 seconds
Final Answer: 48 km/h
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Frequently Asked Questions
Q1: How much time can shortcuts save in SSC CGL?
Answer: Typically 50-70% per question. A 2-minute calculation becomes 30-40 seconds. Over 25 quant questions, this saves 20-25 minutes which can be used for review or difficult questions.
Q2: Which shortcuts are most important for SSC CGL?
Answer: 1) Percentage tricks (most frequent), 2) Multiplication shortcuts (save max time), 3) Approximation techniques (for complex calculations), 4) Vedic squares ending in 5, 5) TSD formulas.
Q3: Will approximation affect accuracy in SSC?
Answer: SSC options are usually designed such that approximation gives correct answer. For close options (1-2% difference), do exact calculation. For options 10%+ apart, approximation is safe and saves time.
Q4: How to practice these shortcuts effectively?
Answer: 1) Learn one category at a time, 2) Practice 10-20 questions daily, 3) Time yourself, 4) Review mistakes, 5) Apply in mock tests, 6) Create your own shortcut sheet.
Q5: Are Vedic math techniques allowed in SSC?
Answer: Yes! Vedic math is just smart calculation methods. There's no restriction on how you calculate, only the final answer matters. These techniques are highly recommended for SSC.
Q6: How to handle calculations without calculator?
Answer: 1) Use approximation first, 2) Break complex calculations into parts, 3) Use multiplication shortcuts, 4) Convert division to multiplication, 5) Keep intermediate steps on paper, 6) Verify with rough check.
Final Exam Strategy for Arithmetic Shortcuts
Time Allocation per question: Without shortcuts: 60-90 seconds, With shortcuts: 20-30 seconds.
Priority Order: 1) Apply percentage tricks, 2) Use Vedic multiplication, 3) Apply approximation, 4) Use formula shortcuts, 5) Do exact calculation only if needed.
Accuracy Check: Verify with approximation, Check units consistency, Ensure answer is reasonable, Cross-check with alternative method if time permits.
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