Mastering Percentages for Problem Solving

Mar 14, 2025

Lecture Notes on Percentages

Introduction

  • Topic: Percentages
  • Importance: Major role in quantitative aptitude for various topics (e.g., time and work, time and distance, simple interest).
  • Focus on mastering basics for effective problem-solving.
  • Overview of upcoming lessons:
    • Lesson 2: Basic questions
    • Lesson 3: Important formulas
    • Lesson 4: Salary calculations
    • Lesson 5: Math-related percentages
    • Lesson 6: Candidate weights

Understanding Percentage

  • Definition: Percentage is a way of expressing a number as a fraction of 100.
  • Techniques for calculating percentages:
    • Normal method vs. Mind calculation.

Example 1: 50% of 2800

  • Normal Method:
    • Write: 50% of 2800
    • Formula: 50/100 * 2800
    • Calculation: Cancel zeros, then multiply 50 by 28.
    • Answer: 1400
  • Mind Calculation:
    • Recognize 50% is half of the number.
    • Answer: 1400

Example 2: 10% of 2800

  • Normal Method:
    • Write: 10% of 2800
    • Formula: 10/100 * 2800
    • Calculation: Cancel zeros, multiply 28 by 10.
    • Answer: 280
  • Mind Calculation:
    • Place one decimal point in 2800 (to get 280).
    • Answer: 280

Other Percentage Calculations

  • 30% of 2800:
    • Normal Method:
      • 30% = 30/100 * 2800 = 840
    • Mind Calculation:
      • 10% = 280, then 30% = 280 * 3 = 840
  • 5% of 2800: Half of 10% (140).
  • 20% of 2800: Double the 10% (560).

Practice

  • Suggested to practice with different numbers.
  • Start with simple numbers before moving to complex calculations.

Important Properties

  • Fundamental property: X% of Y = Y% of X.
  • Example:
    • Finding 6% of 50:
      • Difficult for beginners, but can use the property to find 50% of 36.
      • Answer: 18
  • Example: 20% of 96
    • Direct method: Find 10% (9.6) and then double it for 20%.

Conclusion

  • This lecture provided an introduction to percentages, focusing on understanding and calculating them effectively.
  • Encouragement to view subsequent lessons for deeper understanding.
  • Reminder to practice regularly for proficiency in mind calculations and problem-solving.

Additional Resources

  • Visit YouTube channel for playlist on percentages.
  • Website for comprehensive learning materials on percentages.

Thank you for attending this lecture!