⚡ Shortcuts & Tricks - Complete Compilation

Master these shortcuts to solve questions in <30 seconds! Time is everything in IBPS exams.

🎯 Why Shortcuts Matter

IBPS PO Prelims: 35 Quant questions in 20 minutes = 34 seconds per question!

Without shortcuts: Impossible ❌ With shortcuts: Achievable! ✅

💰 Simple & Compound Interest Shortcuts

SI Shortcut 1: Doubling Time

Time for amount to double = 100/R years

Example: At 5% → 100/5 = 20 years
         At 10% → 100/10 = 10 years

SI Shortcut 2: When SI = Principal

If SI = P, then RT = 100

Quick check:
R = 5%, T = 20 years → RT = 100 ✓
R = 10%, T = 10 years → RT = 100 ✓

CI Shortcut 1: Rule of 72

Time to double with CI ≈ 72/R years

Example: At 8% → 72/8 = 9 years
         At 12% → 72/12 = 6 years

CI Shortcut 2: Two-Year Difference

Difference between CI and SI for 2 years:
CI - SI = P(R/100)²

Example: P = ₹10,000, R = 10%
CI - SI = 10000(0.1)² = ₹100

📊 Percentage Shortcuts

Shortcut 1: Quick Conversions

Fraction → Percentage (Memorize These!)
1/2 = 50%
1/3 = 33.33%
2/3 = 66.67%
1/4 = 25%
3/4 = 75%
1/5 = 20%
1/6 = 16.67%
1/8 = 12.5%
1/10 = 10%

Shortcut 2: Percentage Increase/Decrease

If price increases by 25%, consumption decreases by:
= 25/(100+25) × 100
= 25/125 × 100
= 20%

Quick Formula: x/(100+x) × 100 for decrease
              x/(100-x) × 100 for increase

Shortcut 3: Successive Percentage

Two changes of +a% and +b%:
Net = a + b + ab/100

Example: +10% and +20%
Net = 10 + 20 + (10×20)/100 = 10 + 20 + 2 = 32%

💹 Profit & Loss Shortcuts

Shortcut 1: Quick Profit% Calculation

If CP = ₹100, then:
Profit% = SP - 100

Example: CP = ₹100, SP = ₹125
Profit% = 125 - 100 = 25% (Direct!)

Shortcut 2: SP from Profit%

If Profit% = 25%:
SP = CP × 125/100 = CP × 5/4

Common Multipliers:
10% profit → × 1.1 or 11/10
20% profit → × 1.2 or 6/5
25% profit → × 1.25 or 5/4
50% profit → × 1.5 or 3/2

Shortcut 3: Discount on MP

If MP = ₹100, then:
Discount% = MP - SP

Example: MP = ₹100, SP = ₹80
Discount% = 100 - 80 = 20% (Direct!)

Shortcut 4: False Weight Trick

If sells at cost but uses false weight:
Profit% = (Error/True weight - Error) × 100

Example: Uses 900g instead of 1000g
Profit% = (100/900) × 100 = 11.11%

⚖️ Ratio & Proportion Shortcuts

Shortcut 1: Componendo-Dividendo

If a/b = c/d, then:
(a+b)/(a-b) = (c+d)/(c-d)

Saves 2-3 steps in solving!

Shortcut 2: Ratio to Actual Values

If ratio is a:b and sum is S:
First part = (a/(a+b)) × S
Second part = (b/(a+b)) × S

Example: Ratio 3:2, Sum = 500
First = (3/5) × 500 = 300
Second = (2/5) × 500 = 200

🍶 Alligation Shortcut

The Alligation Rule (Visual Method)

    C₁          C₂
      \        /
         Mean
      /        \
  (C₂-M)    (M-C₁)

Ratio = (C₂-M):(M-C₁)

Example: Mix ₹10/kg and ₹15/kg to get ₹12/kg

    10          15
      \        /
         12
      /        \
     (15-12)  (12-10)
     =  3    :    2

Answer: 3:2 ratio (in <10 seconds!)

⏰ Time & Work Shortcuts

Shortcut 1: LCM Method

If A does work in 'a' days and B in 'b' days:
Total work = LCM(a, b)
A's one day work = LCM/a
B's one day work = LCM/b
Together = LCM/(LCM/a + LCM/b)

Example: A in 12 days, B in 15 days
LCM = 60
A's rate = 5 units/day
B's rate = 4 units/day
Together = 60/9 = 6.67 days

Shortcut 2: Efficiency Ratio

If Time ratio = m:n
Then Efficiency ratio = n:m (inverse!)

Example: A takes 5 days, B takes 10 days
Time ratio = 5:10 = 1:2
Efficiency = 2:1 (A is twice as efficient!)

📏 Average Shortcuts

Shortcut 1: When All Same

If all numbers increase by 'x':
New average = Old average + x

Shortcut 2: Weighted Average

If n₁ items at avg A₁ and n₂ items at avg A₂:
Combined avg = (n₁A₁ + n₂A₂)/(n₁ + n₂)

Quick visual:
        A₁         A₂
          \       /
      Combined Average
          /       \
      (A₂-Avg)  (Avg-A₁)

Ratio n₁:n₂ = (A₂-Avg):(Avg-A₁)

📐 Mensuration Shortcuts

Circle Quick Formulas

Diameter given? Area = π(D/2)² = πD²/4
Circumference = πD (simpler than 2πr)

Rectangle Diagonal

Diagonal = √(L² + B²)

For 3:4 rectangle → Diagonal : Side = 5:3
For square → Diagonal = Side × √2

🔢 Number System Shortcuts

Divisibility Rules (Memorize!)

2: Last digit even
3: Sum of digits divisible by 3
4: Last two digits divisible by 4
5: Last digit 0 or 5
6: Divisible by both 2 and 3
8: Last three digits divisible by 8
9: Sum of digits divisible by 9
11: (Sum of odd position digits) - (Sum of even position digits) = 0 or multiple of 11

Squares Shortcut

(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²

Quick squares near 50:
47² = (50-3)² = 2500 - 300 + 9 = 2209
53² = (50+3)² = 2500 + 300 + 9 = 2809

🔗 Number Series Shortcuts

Common Patterns

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
Difference: 3, 5, 7, 9, 11, 13, 15, 17, 19...

Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512...

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37...

⚡ Calculation Shortcuts

Multiply by 5

× 5 = × 10 ÷ 2

Example: 86 × 5 = 860 ÷ 2 = 430

Multiply by 25

× 25 = × 100 ÷ 4

Example: 44 × 25 = 4400 ÷ 4 = 1100

Multiply by 11

Two digit: Insert sum in middle
Example: 34 × 11 = 3(3+4)4 = 374

If sum >9, carry over:
68 × 11 = 6(6+8)8 = 6(14)8 = 748

Square Numbers Ending in 5

n5² = n(n+1) | 25

Example:
25² = 2×3 | 25 = 625
35² = 3×4 | 25 = 1225
85² = 8×9 | 25 = 7225

Divide by 5

÷ 5 = × 2 ÷ 10

Example: 345 ÷ 5 = 690 ÷ 10 = 69

🎯 Exam-Specific Speed Tricks

Trick 1: Options Elimination

If answer options are far apart, approximate!

Example: Calculate 47.3 × 9.8
Options: (A) 463.54 (B) 253.24 (C) 553.64 (D) 363.54

Quick: ~50 × 10 = 500
Answer must be close to 500 → (A) 463.54

Trick 2: Last Digit Method

To find last digit of large calculations:
Only multiply last digits!

Example: 347 × 589 × 234
Last digits: 7 × 9 × 4 = 252
Last digit of answer = 2

Trick 3: Percentage of Percentage

10% of 20% = 2% (just multiply: 0.1 × 0.2 = 0.02)
5% of 40% = 2%
25% of 80% = 20%

📊 Quick Reference Table

💡 Practice Strategy

Week 1-2: Learn 5 shortcuts per day Week 3-4: Practice 50 questions using shortcuts Week 5+: Achieve <30 sec per question

Daily Routine:

• Morning: Revise 10 shortcuts (10 min)
• Afternoon: Apply on 20 questions (15 min)
• Evening: Speed drill - 50 questions (25 min)

🚀 Quick Access

🎓 Pro Tips

1. Don’t memorize blindly - Understand the logic
2. Practice daily - 30 minutes of shortcut practice
3. Time yourself - Track improvement weekly
4. Mix topics - Don’t practice one topic in isolation
5. Use in mocks - Apply shortcuts in full-length tests

Remember: Shortcuts + Practice = Speed + Accuracy = Selection! 🎯

Master these shortcuts and solve questions in half the time! ⚡