100+ Aptitude Shortcut Tricks for Placement 2026 - Complete Reference

Last Updated: March 2026

Speed is crucial in placement aptitude tests. This comprehensive reference sheet contains 100+ shortcut tricks covering Speed Maths, Vedic Maths, Quick Calculations, Percentages, Ratios, and more to help you solve problems faster and attempt more questions.

Multiplication Shortcuts
Squaring Numbers
Division Tricks
Percentage Shortcuts
Ratio & Proportion Tricks
Number Series Shortcuts
Time-Speed-Distance Shortcuts
Profit & Loss Shortcuts
Time & Work Shortcuts
Data Interpretation Quick Calcs

Multiplication Shortcuts

Trick 1: Multiply by 11

Rule: Add adjacent digits, place sum between them

Example: 45 × 11

4 (4+5) 5 = 495

Example: 67 × 11

6 (6+7) 7 = 6 13 7 = 737 (carry over if sum > 9)

Trick 2: Multiply by 5

Rule: Divide by 2, then multiply by 10 (or add zero)

Example: 46 × 5

46 ÷ 2 = 23
23 × 10 = 230

Trick 3: Multiply by 25

Rule: Divide by 4, multiply by 100

Example: 84 × 25

84 ÷ 4 = 21
21 × 100 = 2100

Trick 4: Multiply by 125

Rule: Divide by 8, multiply by 1000

Example: 96 × 125

96 ÷ 8 = 12
12 × 1000 = 12000

Trick 5: Multiply by 9, 99, 999

Rule: Multiply by (10-1), (100-1), (1000-1)

Example: 37 × 99

37 × 100 = 3700
3700 - 37 = 3663

Example: 58 × 999

58 × 1000 = 58000
58000 - 58 = 57942

Trick 6: Multiply Numbers Ending in 5

Rule: If both end in 5, multiply first parts, add half their sum, append 25

Example: 35 × 45

3 × 4 = 12
(3+4)÷2 = 3.5 → add: 12 + 3 = 15, remainder 1
Actually easier: 35 × 45 = 35 × (40 + 5) = 1400 + 175 = 1575

Better Method: (n1 × n2) + 25 where n are tens digits 35 × 45: (3×4) + (3+4)/2 = 12 + 3.5 → Use: (30+5)(40+5) = 1200 + 150 + 200 + 25 = 1575

Trick 7: Multiply Complementary Numbers (Sum to 100, 1000)

Rule: If a+b=100, a×b = (50+(a-50)) × (50-(a-50)) = 2500 - (a-50)²

Example: 43 × 57 (43+57=100)

43 × 57 = 2500 - 49 = 2451

Trick 8: Criss-Cross Method (2-digit × 2-digit)

Example: 23 × 45

Unit digits: 3×5 = 15, write 5, carry 1
Cross: (2×5)+(3×4) = 10+12 = 22, plus carry 1 = 23, write 3, carry 2
First digits: 2×4 = 8, plus carry 2 = 10
Answer: 1035

Squaring Numbers

Trick 9: Square Numbers Ending in 5

Rule: n × (n+1), append 25

Example: 35²

3 × 4 = 12
Append 25: 1225

Example: 85²

8 × 9 = 72
7225

Trick 10: Square Numbers Near 50

Rule: (25 + extra) / (extra)² (2 digits for square part)

Example: 53² (3 more than 50)

25 + 3 = 28
3² = 09
2809

Example: 48² (2 less than 50)

25 - 2 = 23
(-2)² = 04
2304

Trick 11: Square Numbers Near 100

Rule: (Number + difference) / (difference)²

Example: 96² (4 less than 100)

96 - 4 = 92
4² = 16
9216

Example: 108² (8 more than 100)

108 + 8 = 116
8² = 64
11664

Trick 12: Square Using (a+b)² Formula

Example: 42² = (40+2)² = 1600 + 160 + 4 = 1764

Example: 67² = (70-3)² = 4900 - 420 + 9 = 4489

Division Tricks

Trick 13: Divide by 5

Rule: Multiply by 2, divide by 10

Example: 230 ÷ 5

230 × 2 = 460
460 ÷ 10 = 46

Trick 14: Divide by 25

Rule: Multiply by 4, divide by 100

Example: 750 ÷ 25

750 × 4 = 3000
3000 ÷ 100 = 30

Trick 15: Divide by 125

Rule: Multiply by 8, divide by 1000

Example: 4000 ÷ 125

4000 × 8 = 32000
32000 ÷ 1000 = 32

Percentage Shortcuts

Trick 16: Common Percentage Values

Percentage	Fraction	Decimal
50%	1/2	0.5
25%	1/4	0.25
75%	3/4	0.75
12.5%	1/8	0.125
37.5%	3/8	0.375
62.5%	5/8	0.625
87.5%	7/8	0.875
33.33%	1/3	0.333
66.67%	2/3	0.667
16.67%	1/6	0.167

Trick 17: Calculate 10%, 5%, 1%

10%: Move decimal one place left
5%: 10% ÷ 2
1%: Move decimal two places left

Example: 15% of 480

10% = 48
5% = 24
15% = 48 + 24 = 72

Trick 18: Successive Percentage Change

Rule: a + b + (a×b)/100

Example: Price increased by 20%, then by 10%

Net change = 20 + 10 + (20×10)/100 = 30 + 2 = 32% increase

Example: Increased 20%, then decreased 10%

Net change = 20 - 10 + (20×-10)/100 = 10 - 2 = 8% increase

Trick 19: Percentage Change Formula

% Change = (Change/Original) × 100

Example: From 80 to 100

Change = 20
% Change = (20/80) × 100 = 25% increase

Trick 20: If A is R% more than B, B is less than A by:

Formula: [R/(100+R)] × 100

Example: A is 25% more than B

B is less than A by: (25/125) × 100 = 20%

Trick 21: If A is R% less than B, B is more than A by:

Formula: [R/(100-R)] × 100

Example: A is 20% less than B

B is more than A by: (20/80) × 100 = 25%

Ratio & Proportion Tricks

Trick 22: Dividing Amount in Ratio

Example: Divide ₹840 in ratio 3:4

Total parts = 7
First part = (3/7) × 840 = 360
Second part = (4/7) × 840 = 480

Trick 23: Third Proportional

If a:b = b:c, then c is third proportional c = b²/a

Example: Third proportional to 4 and 6

c = 36/4 = 9

Trick 24: Fourth Proportional

If a:b = c:d, find d d = bc/a

Example: Fourth proportional to 2, 3, 4

d = (3×4)/2 = 6

Trick 25: Mean Proportional

Between a and b: √(ab)

Example: Mean proportional between 4 and 9

√(36) = 6

Trick 26: Comparing Ratios

Convert to same denominator or cross-multiply

Example: Compare 3:4 and 5:7

3×7 = 21, 4×5 = 20
Since 21 > 20, 3:4 > 5:7

Number Series Shortcuts

Trick 27: Difference Method

Find difference between consecutive terms

Example: 2, 5, 10, 17, 26, ?

Differences: 3, 5, 7, 9, 11
Next term: 26 + 11 = 37

Trick 28: Difference of Differences

When first differences don't reveal pattern

Example: 1, 4, 10, 19, 31, ?

First differences: 3, 6, 9, 12
Second difference: 3 (constant)
Next first difference: 15
Next term: 31 + 15 = 46

Trick 29: Square/Cube Patterns

Example: 1, 4, 9, 16, 25, ?

1², 2², 3², 4², 5², 6² = 36

Example: 1, 8, 27, 64, 125, ?

1³, 2³, 3³, 4³, 5³, 6³ = 216

Trick 30: Prime Numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...

Trick 31: Fibonacci Series

Each term = sum of previous two 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

Trick 32: Geometric Progression

Each term × constant ratio Example: 2, 6, 18, 54, ? (×3)

Next: 162

Time-Speed-Distance Shortcuts

Trick 33: Speed Conversion

km/h to m/s: Multiply by 5/18
m/s to km/h: Multiply by 18/5

Example: 72 km/h = 72 × (5/18) = 20 m/s

Trick 34: Average Speed (Same Distance)

Formula: 2xy/(x+y)

Example: Go at 30 km/h, return at 60 km/h

Average speed = (2×30×60)/(30+60) = 3600/90 = 40 km/h

Trick 35: Relative Speed (Same Direction)

Relative Speed = Faster - Slower

Example: Train A: 80 km/h, Train B: 60 km/h (same direction)

Relative speed = 80 - 60 = 20 km/h

Trick 36: Relative Speed (Opposite Direction)

Relative Speed = Sum of speeds

Example: Two trains 80 km/h and 70 km/h towards each other

Relative speed = 80 + 70 = 150 km/h

Trick 37: Train Crossing Time

Time = (Length1 + Length2) / Relative Speed

Profit & Loss Shortcuts

Trick 38: Basic Formulas

Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100
SP = CP × (100 + P%)/100
CP = SP × 100/(100 + P%)

Trick 39: Selling at Same Price with Different Profits

If two items sold at same price, one at x% profit, other at x% loss: Overall Loss % = x²/100

Example: Two items sold at ₹100 each, one at 20% profit, one at 20% loss

Loss % = 400/100 = 4% loss

Trick 40: False Weights

If shopkeeper sells at cost price but uses weight less by x%: Gain % = [x/(100-x)] × 100

Example: Uses 900g for 1kg

Gain % = (100/900) × 100 = 11.11%

Trick 41: Successive Discounts

Equivalent Discount = a + b - (ab/100)

Example: 20% and 10% successive discounts

Equivalent = 20 + 10 - 2 = 28%

Time & Work Shortcuts

Trick 42: Work Rate

If A can do work in x days, A's 1 day work = 1/x

Trick 43: Combined Work

If A does in x days, B in y days:

Together: xy/(x+y) days
Or per day: (x+y)/xy work

Example: A in 6 days, B in 12 days

Together: (6×12)/(6+12) = 72/18 = 4 days

Trick 44: Three Workers

A in x days, B in y days, C in z days:

Together: xyz/(xy+yz+zx) days

Trick 45: Work & Wages

Wages distributed in inverse ratio of time taken

Example: A in 10 days, B in 15 days, total wage ₹1500

Ratio: 15:10 = 3:2
A gets: (3/5) × 1500 = ₹900
B gets: ₹600

Trick 46: Men-Days Work

M1 × D1 = M2 × D2 (same work)

Example: 10 men complete in 12 days

15 men will take: (10×12)/15 = 8 days

Data Interpretation Quick Calcs

Trick 47: Approximation

When options are far apart, approximate

Example: 47.8% of 312.5

≈ 50% of 300 = 150
(Actual: 149.375)

Trick 48: Fraction to Percentage

Keep common fractions memorized

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.67%
1/8	12.5%
1/9	11.11%
1/12	8.33%

Trick 49: Quick Addition

Pair numbers that sum to 10, 100, etc.

Example: 17 + 23 + 45 + 55 + 32

(17+23) + (45+55) + 32
40 + 100 + 32 = 172

Trick 50: Digital Root (Divisibility Check)

Sum digits until single digit

Digital root 9: divisible by 9
Digital root 3, 6, 9: divisible by 3

Additional Quick Tricks (51-100)

Algebra Shortcuts

Trick 51: a² - b² = (a+b)(a-b)

Trick 52: (a+b)² = a² + 2ab + b²

Trick 53: (a-b)² = a² - 2ab + b²

Trick 54: a³ + b³ = (a+b)(a² - ab + b²)

Trick 55: a³ - b³ = (a-b)(a² + ab + b²)

Trick 56: If x + 1/x = k, then x² + 1/x² = k² - 2

Trick 57: Sum of first n natural numbers: n(n+1)/2

Trick 58: Sum of first n odd numbers: n²

Trick 59: Sum of first n even numbers: n(n+1)

Trick 60: Sum of squares: n(n+1)(2n+1)/6

Divisibility Rules

Trick 61: Divisible by 2: Last digit even

Trick 62: Divisible by 3: Sum of digits divisible by 3

Trick 63: Divisible by 4: Last two digits divisible by 4

Trick 64: Divisible by 5: Last digit 0 or 5

Trick 65: Divisible by 6: Divisible by both 2 and 3

Trick 66: Divisible by 8: Last three digits divisible by 8

Trick 67: Divisible by 9: Sum of digits divisible by 9

Trick 68: Divisible by 11: Difference of odd and even place sums divisible by 11

LCM & HCF

Trick 69: LCM × HCF = Product of two numbers

Trick 70: HCF of fractions: HCF of numerators/LCM of denominators

Trick 71: LCM of fractions: LCM of numerators/HCF of denominators

Averages

Trick 72: Average of first n natural numbers: (n+1)/2

Trick 73: If each number increases by x, average increases by x

Trick 74: If average of n numbers is A, sum = n × A

Trick 75: Average speed = Total Distance/Total Time (not average of speeds)

Mixtures & Alligations

Trick 76: Alligation Rule: (Cheaper quantity):(Dearer quantity) = (d-m):(m-c) Where m = mean price, c = cheaper, d = dearer

Trick 77: Replacement formula: Final amount = Initial(1 - x/n)^t Where x = replaced quantity, n = total, t = times

Simple & Compound Interest

Trick 78: SI = (P×R×T)/100

Trick 79: CI = P[(1+R/100)^T - 1]

Trick 80: CI - SI for 2 years = P(R/100)²

Trick 81: CI - SI for 3 years = P(R/100)² × (3 + R/100)

Trick 82: Amount doubles in 72/R years (Rule of 72, approximate)

Permutation & Combination

Trick 83: nPr = n!/(n-r)!

Trick 84: nCr = n!/(r!(n-r)!)

Trick 85: nCr = nC(n-r)

Trick 86: Circular permutation: (n-1)!

Probability

Trick 87: Probability = Favorable/Total

Trick 88: P(A or B) = P(A) + P(B) - P(A and B)

Trick 89: P(A and B) = P(A) × P(B) for independent events

Trick 90: At least one probability = 1 - P(none)

Clocks

Trick 91: Hour hand moves 0.5° per minute

Trick 92: Minute hand moves 6° per minute

Trick 93: Relative speed: 5.5° per minute

Trick 94: Hands coincide 22 times in 24 hours

Trick 95: Hands at right angles 44 times in 24 hours

Calendars

Trick 96: Odd days determine day of week

Trick 97: 100 years = 5 odd days (76 ordinary + 24 leap)

Trick 98: 200 years = 3 odd days

Trick 99: 300 years = 1 odd day

Trick 100: 400 years = 0 odd days

Practice Problems with Shortcuts

Problem 1

Find 35 × 35 Using Trick 9: 3 × 4 = 12, append 25 → 1225

Problem 2

A train travels 60 km at 30 km/h and 60 km at 60 km/h. Find average speed. Using Trick 34: 2×30×60/(30+60) = 40 km/h

Problem 3

Price first increases 25% then decreases 20%. Net effect? Using Trick 18: 25 - 20 + (25×-20)/100 = 5 - 5 = No change

Problem 4

12 men complete work in 8 days. 16 men will take? Using Trick 46: (12×8)/16 = 6 days

Problem 5

Find 15% of 240 Using Trick 17: 10% = 24, 5% = 12, 15% = 24+12 = 36

FAQs

Q1: How many shortcut tricks should I memorize?

A: Focus on 20-30 most commonly used tricks. Practice them until they become automatic.

Q2: Will using shortcuts lead to mistakes?

A: Only if applied incorrectly. Always verify with traditional method when learning.

Q3: Which tricks are most important for placements?

A: Percentages, ratios, time-speed-distance, time-work, and quick multiplication are most frequently used.

Q4: How to practice these shortcuts?

A: Apply them in mock tests. Start with easy problems, then use for harder ones.

Q5: Can I use calculators in placement tests?

A: Most tests don't allow calculators. These shortcuts are essential for speed.

Practice these shortcuts daily. Speed in aptitude comes from pattern recognition and technique, not just knowledge. Master these tricks and watch your scores improve!