CDS 2027 - Paper 3: Elementary Mathematics cheat sheet for Arithmetic! 📱 Practice 1 Lakh+ PYQs on ExamBhai.com! - Free Study Material

Chapter Summary: Core Arithmetic Principles

Mastering Elementary Mathematics for the CDS examination requires a strong foundation in arithmetic concepts, quick formula recall, and rapid calculation techniques.

1. Number System & Divisibility

The system of real numbers forms the basis of arithmetic calculations. Understanding properties of prime numbers, factors, and divisibility rules helps in solving complex simplification problems quickly.

• LCM & HCF: For two numbers \(a\) and \(b\), the relationship is given by: \[\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b\]
• Divisibility: A number is divisible by 3 if the sum of its digits is divisible by 3; divisible by 11 if the difference between the sum of digits at odd places and even places is 0 or a multiple of 11.

2. Percentages, Profit & Loss

Percentage represents a fraction with a denominator of 100, serving as the core component for calculating interest, discounts, and profit margins.

• Percentage Change: \[\text{Percentage Increase/Decrease} = \bigl(\frac{\text{Absolute Change}}{\text{Original Value}}\bigr) \times 100\]
• Profit & Loss: Profit percentage is calculated on Cost Price (CP): \[\text{Profit \%} = \bigl(\frac{\text{Selling Price} - \text{CP}}{\text{CP}}\bigr) \times 100\]

3. Ratio, Proportion & Averages

Ratios express relative sizes between quantities, while averages represent the central tendency of a given dataset.

• Average: \[\text{Average} = \frac{\text{Sum of all observations}}{\text{Total number of observations}}\]
• Compound Interest: For principal \(P\), rate \(R\%,\) and time \(n\) years: \[A = P \bigl(1 + \frac{R}{100}\bigr)^n\]

4. Time, Speed & Distance

Problems involving motion require converting units accurately between \(\text{km/h}\) and \(\text{m/s}\).

• Basic Relation: \[\text{Speed} = \frac{\text{Distance}}{\text{Time}}\]
• Unit Conversion: \(1 \text{ km/h} = \frac{5}{18} \text{ m/s}\)

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