RRB PREP
NTPC ALP Group D

Arithmetic for RRB Exams

Number System

Key Concepts

  • • Natural Numbers: 1, 2, 3, ...
  • • Whole Numbers: 0, 1, 2, 3, ...
  • • Integers: ..., -2, -1, 0, 1, 2, ...
  • • Prime Numbers: Divisible only by 1 and itself (e.g., 2, 3, 5, 7, 11)
  • • Co-prime Numbers: Two numbers having HCF = 1

Divisibility Rules

  • • By 2: Last digit is 0, 2, 4, 6, 8
  • • By 3: Sum of digits is divisible by 3
  • • By 4: Last two digits divisible by 4
  • • By 5: Last digit is 0 or 5
  • • By 8: Last three digits divisible by 8
  • • By 9: Sum of digits divisible by 9
  • • By 11: (Sum of odd place digits) - (Sum of even place digits) = 0 or divisible by 11

HCF & LCM

Formulas

  • • Product of two numbers = HCF × LCM
  • • HCF of Fractions = (HCF of Numerators) / (LCM of Denominators)
  • • LCM of Fractions = (LCM of Numerators) / (HCF of Denominators)

Percentage

Important Conversions

1/2 = 50%
1/3 = 33.33%
1/4 = 25%
1/5 = 20%
1/6 = 16.66%
1/8 = 12.5%
1/10 = 10%
1/20 = 5%

Formulas

  • • % Increase = (Increase / Original Value) × 100
  • • % Decrease = (Decrease / Original Value) × 100
  • • If A is x% more than B, then B is [x / (100+x) × 100]% less than A
  • • If A is x% less than B, then B is [x / (100-x) × 100]% more than A

Profit & Loss

Basic Formulas

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

Discount

  • • Discount = MP - SP
  • • Discount % = (Discount / MP) × 100
  • • Successive Discounts: x% and y% = (x + y - xy/100)%

Simple & Compound Interest

Simple Interest (SI)

SI = (P × R × T) / 100

Amount = P + SI

Compound Interest (CI)

Amount = P(1 + R/100)n

CI = Amount - Principal

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

Time, Speed & Distance

Formulas

  • • Distance = Speed × Time
  • • Speed = Distance / Time
  • • Time = Distance / Speed
  • • Average Speed = (2xy) / (x+y) (for equal distances at speeds x and y)

Conversions

  • • km/hr to m/s: Multiply by 5/18
  • • m/s to km/hr: Multiply by 18/5

Trains

  • • Relative Speed (Opposite Direction) = S1 + S2
  • • Relative Speed (Same Direction) = S1 - S2
  • • Time to cross = (Length of Train + Length of Object) / Relative Speed

Test Your Knowledge

30 random questions • 1 minute per question