Arithmetic Formulas Cheat Sheet for CAT

Preparing for the CAT exam requires mastering Quantitative Aptitude, and Arithmetic plays a vital role in this section. Whether you’re enrolled in CAT coaching in Delhi or studying on your own, having a handy collection of important arithmetic formulas can drastically improve your problem-solving speed and accuracy. This cheat sheet compiles the essential formulas you must remember to boost your performance in arithmetic questions.

 Percentage, Profit & Loss Formulas

- Percentage Formula: $$ \text{Percentage} = \frac{\text{Value}}{\text{Total Value}} \times 100 $$ 

- Profit & Loss: 

  - Profit = Selling Price (SP) – Cost Price (CP) 

  - Profit % = $$ \frac{\text{Profit}}{\text{CP}} \times 100 $$ 

  - Loss % = $$ \frac{\text{Loss}}{\text{CP}} \times 100 $$

These formulas are frequently tested in topics like successive percentage change and discount problems.

 Ratio, Proportion, and Partnership

- Ratio: $$ a : b = \frac{a}{b} $$ 

- Proportion: $$ \frac{a}{b} = \frac{c}{d} $$ 

- Partnership: 

  - When Time is same → Profit ∝ Investment 

  - When Time differs → Profit ∝ Investment × Time 

Candidates preparing with top CAT coaching in Delhi often find that mastering ratio and proportion helps them in complex data interpretation and mixture problems as well.

Simple and Compound Interest Formulas

- Simple Interest (SI): $$ SI = \frac{P \times R \times T}{100} $$ 

- Compound Interest (CI): $$ CI = P(1 + \frac{R}{100})^T - P $$ 

Focus on understanding the difference between SI and CI, as CAT often includes conceptual questions rather than direct formula-based ones.

Time, Speed, and Distance

- Speed = Distance / Time 

- Average Speed: $$ \frac{2xy}{x + y} $$ (for two equal distances at different speeds) 

- Work Formula: $$ \text{Work} = \text{Rate} \times \text{Time} $$ 

 

These formulas are extremely useful for motion and work-time problems that form a major part of the arithmetic syllabus.

Final Tip

Arithmetic is not about memorizing formulas but applying them efficiently during the test. Revising this cheat sheet daily and practicing questions regularly can enhance your quantitative accuracy. So, whether you’re revising after class or preparing independently, make sure these formulas become second nature before the CAT exam.

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