Quick Revision Sheet: Arithmetic Shortcuts for RRB Exams

1. Number System & Simplification

• BODMAS → Bracket, Order, Division, Multiplication, Addition, Subtraction
• Divisibility Rules
  • 2: last digit 0/2/4/6/8
  • 3: sum of digits divisible by 3
  • 5: ends 0/5
  • 9: sum of digits divisible by 9
• Unit digit cycle (repeat every 4 powers)
  • 2: 2,4,8,6
  • 3: 3,9,7,1
  • 7: 7,9,3,1
  • 8: 8,4,2,6

Shortcut
To find unit digit of 3⁵⁷ → 57 mod 4 = 1 → 3¹ = 3

2. LCM & HCF

• Product of two numbers = LCM × HCF
• Co-primes: HCF = 1
• Fractions
  • LCM = LCM(num) / HCF(den)
  • HCF = HCF(num) / LCM(den)

Mnemonic
“Large LCM, Humble HCF”

3. Percentage

• Base-shift formula: New value = Old × (100 ± x)/100
• Successive % change: net = x + y + xy/100
• Fraction ↔ %
  1/3 = 33.33%, 1/7 ≈ 14.28%, 1/15 ≈ 6.67%

Shortcut
42% of 250 → 4.2 × 25 = 105

4. Profit & Loss

• SP = CP × (100 ± P/L%)
• Discount % = (MP – SP)/MP × 100
• Overall gain/loss when two items sold at same SP & same %: always loss % = (common %)²/100

Mnemonic
“CP is always 100; add profit, subtract loss.”

5. Simple & Compound Interest

Rule of 72
Years to double = 72 / rate %

6. Ratio & Proportion

• Componendo: a/b = c/d ⇒ (a+b)/b = (c+d)/d
• Dividendo: (a–b)/b = (c–d)/d
• Alligation
  • CP of mix = (q₁c₁+q₂c₂)/(q₁+q₂)
  • Ratio = (high–mean) : (mean–low)

7. Time & Work

• Work = 1 (total work)
• If A does in x days, 1-day work = 1/x
• Combined 1/x + 1/y = 1/T
• Efficiency trick: If men ↑, days ↓ (M₁D₁ = M₂D₂)

Mnemonic
“MDH formula: M₁D₁H₁ = M₂D₂H₂”

8. Time, Speed & Distance

• Distance = Speed × Time
• Average speed (same distance): 2xy/(x+y)
• Relative speed
  • Same direction: subtract
  • Opposite: add
• Train crossing: Distance = train length + platform length

Quick Table

| km/h → m/s | × 5/18 | | m/s → km/h | × 18/5 |

9. Average & Allegation

• Average = Sum / n
• Weighted avg = Σ(wᵢxᵢ)/Σwᵢ
• Age problem: new member added → total age ↑ by n × change in avg

Shortcut
If avg of 20 numbers is 30 and two removed numbers sum to 68, new avg = (600 – 68)/18 = 29.55

10. Boats & Streams

• Downstream speed = u + v
• Upstream speed = u – v
• Still water speed u = (D+U)/2
• Stream speed v = (D–U)/2

11. Permutation & Combination

• nPr = n!/(n–r)!
• nCr = n!/(r!(n–r)!)
• Handy: nCr = nC(n–r)
• Arrangement around circle: (n–1)!

12. Probability

• P = Favourable / Total
• At least one = 1 – P(none)
• Coin: 2ⁿ outcomes
• Dice: 6ⁿ outcomes

Common Exam Q&A (Quick-fire)

30-Second Rapid Table

Last tip: In options, pick the “round” number first; calculator-banned exam loves divisible answers.