Percentages, Taxes, and Simple Interest

Jul 22, 2024

Chapter 14: Percentages

Introduction to Percentages

  • Importance: Understanding and comparing quantities.
  • Example: Comparison of marks obtained by Sita and Mita.

Concept of Percentages

  • Definition: Fraction with a denominator of 100.
  • Example: 8% means 8/100.
  • Percentage sign (%): Symbol that represents division by 100.

Converting Fractions to Percentages

  • Multiply and divide by 100.
  • Example: 2/5 = 2/5 * 100 = 40%.

Converting Decimals to Percentages

  • Multiply by 100 and move the decimal point two places to the right.
  • Examples:
    • 0.9 = 90%
    • 2.8 = 280%

Converting Percentages to Fractions

  • Reverse process: divide by 100.
  • Example: 45% = 45/100.

Converting Percentages to Decimals

  • Move the decimal place two places to the left.
  • Examples:
    • 45% = 0.45
    • 223% = 2.23

Converting Percentages to Ratios and Vice Versa

  • Percentages can be written as ratios.
  • Example: 24% = 6/25 = 6:25.

Practical Applications of Percentages

Finding Part of a Total

  • Example: 8% of 400 = 400 * 8/100 = 32.

Given Percentage and Part, Find the Total

  • Example: Given 8% is 32, find total is 32 * 100/8 = 400.

Given Part and Total, Find the Percentage

  • Example: 32 out of 400 = 32/400 * 100 = 8%.

Taxes

Introduction

  • Governments collect taxes to fund activities like infrastructure, salaries, etc.
  • Types: Direct and Indirect taxes.

Direct Taxes

  • Examples: Rates, customs duty, income tax.

Indirect Taxes

  • Examples: Value-added Tax (VAT).

Rates

  • Charged by local councils for properties.
  • Example Calculation: Assessed value, find annual or quarterly rates.

Customs Duty

  • Charged on imports and exports.
  • Example: 10% duty on a clock worth 5000 = 500.

Income Tax

  • Varies by annual income and ranges.
  • Table example for 2011.
  • Example Calculation: Calculate tax for given income.

VAT

  • Charged on goods and services.
  • Example: 15% VAT on a bill, calculate the total amount payable.

Simple Interest

  • Definition: Interest calculated on the initial principal amount.

Simple Interest Formula

  • Interest = Principal (P)
  • Rate (R)
  • Time (T) / 100.

Examples

  • Calculations for different scenarios like loan settlements, finding time or amount paid.

Exercises

  • Solving problems related to percentages, taxes, and simple interest.