📘 Shortcut Tricks for Competitive Exams

🧮 Percentage

Divide by 20 or multiply by 0.05
Example: 5% of 400 = 400 ÷ 20 = 20

👷 Time & Work

Use Man-Days formula: Work = Men × Days. Use ratios for faster solving.

💰 Profit & Loss

Successive Discount Formula:
(A + B + AB/100)
Example: 10% and 20% = 10 + (-20) + (-10×20)/100 = -28%

📐 LCM & HCF

Prime factorization method:
LCM = product of highest powers
HCF = product of lowest powers

🧠 Square of Numbers Ending in 5

Use: (x5)² = x × (x + 1), then add 25
Example: 65² = 6×7 = 42 → 4225

🔡 Coding-Decoding

Use Reverse Alphabet Position:
A = 26, B = 25 ... Z = 1
Example: C = 24, D = 23

📆 Calendar Trick

Odd Day Method: Total days ÷ 7 = Quotient + Remainder = Odd Days
Use this to find days of week quickly.

💨 Speed-Time-Distance

Shortcut: Distance = (Speed × Time)
Use ratio comparison for relative speed problems.

📊 Averages

Trick: Average = (Sum of terms) ÷ (No. of terms)
Use deviation method for fast calculation.

💱 Ratio & Proportion

Cross multiplication: a:b = c:d → a×d = b×c
Apply in mixtures, ages, and work sharing problems.

🏦 Simple Interest

Formula: SI = (P × R × T)/100
Use direct calculation when one value is rounded.

📈 Compound Interest

Formula: CI = P(1 + R/100)^T
For 2 years, use shortcut: CI ≈ SI + (SI × R)/100

🧩 Number Series

Identify patterns like addition, multiplication, squares, cubes. Break down by gaps between numbers.

📦 Mixture & Alligation

Use Alligation Rule:
(C1 - Mean):(Mean - C2) = Quantity Ratio
Example: Cost of mix = ₹30 from ₹20 and ₹50 in 1:1 ratio.

🧮 Multiplication Trick

Use Vedic Math shortcut: (a + b)(a - b) = a² - b²
Example: 102 × 98 = (100 + 2)(100 - 2) = 100² - 4 = 9996

🕒 Clocks

Angle = |(30 × hour − 11/2 × minutes)|
Example: 3:15 → |(30×3 − 11/2×15)| = |90 − 82.5| = 7.5°

👪 Blood Relations

Use family tree. Decode step-by-step: e.g., “A is B’s brother’s son” → A is B’s nephew.

🧭 Direction Sense

Assume initial direction as North. Turn left = anti-clockwise, right = clockwise. Use basic compass diagram.

🔁 Syllogism

Use Venn diagrams. Key rules:
All A are B = overlap
Some A are B = partial intersection
No A is B = disjoint sets.

🎂 Age Problems

Assume present age as x. Translate statements into equations.
Tip: Use "x + age difference" or "2x = father’s age" formats.

📏 Geometry Area Shortcut

Square: A = a², Rectangle: A = l × b
Circle: A = πr²
Triangle: A = ½ × b × h

🚣 Boats & Streams

Downstream Speed = u + v
Upstream Speed = u − v
Distance = Speed × Time

🚆 Trains

Formula: Distance = Speed × Time
Convert km/hr to m/s: ×(5/18)
Use relative speed when 2 trains move opposite.

🧮 Simplification

Use BODMAS:
Brackets, Order, Division, Multiplication, Addition, Subtraction
Memorize common squares, cubes, fractions.

➕ Digit Sum Method

Sum of digits of a number. Useful for quick verification of answers in calculations, especially with options. If A + B = C, then digit sum(A) + digit sum(B) = digit sum(C).

7️⃣ Rule of 72 (for doubling money)

Approximate time for an investment to double: Time = 72 / (Interest Rate %)
Example: At 8% interest, money doubles in approx. 72/8 = 9 years.

🔢 Unit Digit Concept

To find the unit digit of a large power, observe the cyclicity of the unit digits. For example, powers of 2 (2,4,8,6,2,...) have a cycle of 4. Divide the power by 4 and use the remainder as the new power.

🔄 Analogy / Classification (Reasoning)

Identify the relationship between a given pair (e.g., synonym, antonym, cause-effect, part-whole) and apply the same logic to find the missing term or the odd one out.

🪑 Seating Arrangement

Start with definite information (e.g., A is next to B). Use visual diagrams (circles, lines) and mark possibilities/impossibilities to narrow down arrangements.