Percentage Lecture Notes

Introduction to Percentages

• Importance of understanding percentages in quantitative aptitude.
• Topics covered in upcoming lessons:
  • Lesson 2: Solving basic questions.
  • Lesson 3: Important formulas related to percentages.
  • Lesson 4: Applications in salary calculations.
  • Lesson 5: Mathematical applications.
  • Lesson 6: Candidate waters (possible context-specific application).

Basics of Percentages

• Definition: A percentage represents a fraction out of 100.
• Importance of mastering percentage basics for quick calculations.

Calculating Percentages

Example with 50%

• Calculation of 50% of 2800:
  • Normal Method:
    • Write: 50% of 2800 = ?
    • Formula: 50/100 * 2800
    • Simplifying gives: 1400.
  • Mind Calculation:
    • 50% is half, thus 2800/2 = 1400.*

Example with 10%

• Calculation of 10% of 2800:
  • Normal Method:
    • Write: 10% of 2800 = ?
    • Formula: 10/100 * 2800 = 280.
  • Mind Calculation:
    • Simply move the decimal left: 2800 becomes 280.*

General Techniques for Quick Calculations

• For 1%:
  • Place decimal point two places left (2800 -> 28).
• For 10%:
  • Place decimal point one place left (2800 -> 280).
• For 5%:
  • Half of 10% (280 -> 140).
• For 30%:
  • Use known 10% (280) and multiply by 3 (840).
• For 20%:
  • Double 10% (280 x 2 = 560).

Composite Percentages

• Calculate complex percentages by breaking them down.
  • Example: For 35%, think of it as 30% + 5%.
  • Calculate 30% from previous knowledge, then add 5%.

Practice Recommendations

• Start with simple numbers (e.g., 9400, 2800).
• Gradually move to larger numbers (e.g., 2340, 5680).
• Repetition will enhance speed and accuracy.

Important Property of Percentages

• Property: X% of Y = Y% of X.
• Example: 6% of 50 = 50% of 36.
  • Calculation using property simplifies finding percentages.
• Always check if interchanging makes calculations easier.

Conclusion

• Understanding the basics of percentages is crucial for competitive exams and practical applications.
• Follow up with additional lessons for deeper insights.
• Encourage sharing resources for better preparation.