Tutorial on Percentage

Introduction

• Percentage is fundamental in quantitative aptitude.
• Commonly featured in placement tests, job interviews, and competitive exams.
• CareerRight.com has over 1000 aptitude questions for practice.

Understanding Percentage

• Definition: Percentage means part of something and is represented by the symbol '%'.
• Mathematical Representation: Percentage = Part / Whole × 100.
• Example: 25% means 25/100 or a quarter of a whole.

Key Concepts

• Whole Amount: 100% represents the entire quantity.
  • Example: If a biscuit represents the whole (100%), giving 30% means giving a part of it.
• Finding Percentages: To find a percentage of a quantity:
  • Example: 10% of 80 liters of water is found by calculating 10/100 × 80 = 8 liters.
• Common Percentages:
  • Half = 50%
  • One-third = 33.33%
  • One-fourth = 25%
  • One-tenth = 10%
  • One-fifteenth = 6.67%

Calculating Percentages

• Finding 10%: Move the decimal point one place to the left.
  • Example: 10% of 260 = 26.
• Finding 20%: Find 10% then multiply by 2.
• Finding 39%: Calculate 40% then subtract 1%.
  • Example: 39% of 260 = 40% - 1% = 101.4.

Example Problems

1. 56% of Y = 182: Y = (182 × 100) / 56 = 325.
2. What percent is 42 kg of 336 kg?:
   • Percent = (42/336) × 100 = 12.5%.
3. If 15% of Y = 21% of Z, find 12.5% of Y in relation to Z: = (21 × 12.5) / 15 = 17.5%.
4. Price of rice is 30% less than wheat: Calculate how much more wheat costs than rice, resulting in 42.85% more.
5. Change in Price After Increases: Calculate original price changes using assumed values.

Tips for Easy Calculations

• Use fractions instead of decimals for quicker calculations.
• Always relate quantities through percentage calculations by setting up equations.

Closing Thoughts

• Practice different percentage problems to strengthen understanding.
• Regular practice will enable quick solving of percentage questions in exams.
• For further help, refer to CareerRight.com for additional problems and solutions.