Ratio Lecture Notes

Introduction

• Instructor: Ravi Prakash
• Topic: Understanding and applying ratios.

Example 1: Cricket Match Scoring

• Total runs scored by Sachin, Virat, and Yuvi = 570.
• Ratio of Sachin to Yuvi = 3:2.
• Ratio of Yuvi to Virat = 3:2.

Combining Ratios

• Combined ratio of Sachin:Yuvi:Virat.
  • Sachin = 3 * 3 = 9
  • Yuvi = 2 * 3 = 6
  • Virat = 2 * 2 = 4
  • Final ratio: 9:6:4.

Calculating Runs

• Total parts = 9 + 6 + 4 = 19.
• Each part = 570 / 19 = 30.
• Sachin's score = 9 * 30 = 270.
  • Answer: Sachin scored 270 runs.

Example 2: Salary Ratios

• Salary ratios:
  • January to February = 1.5:1.33.
  • February to March = 2:2.67.

Converting Ratios

• Convert decimals to fractions:
  • 1.5 = 3/2, 1.33 = 4/3, 2.67 = 8/3.
• Ratio of January:February = 9:8.
• Ratio of February:March = 3:4.

Combined Ratios

• Combined ratio of January:February:March:
  • Results in 27:24:32.

Salary Calculations

• January: 27 units.
• March: 32 units.
• Difference = 32 - 27 = 5 units = 90.
  • 1 unit = 18 (90/5).
• Total salary for 3 months = 83 units.
  • 83 * 18 = 1494.
• Bonus = 40% of 1494 = 597.6.
  • Answer: Bonus is 597.6.

Example 3: Students Ratio

• Total students = 660.
• Ratio of boys to girls = 13:9.

Initial Calculations

• Total parts = 22 (13 + 9).
• Boys = 660 * (13/22) = 390.
• Girls = 660 * (9/22) = 270.

Changes in Students

• 30 girls join, some boys leave.
• New ratio = 6:5.
• New number of girls = 300.
• New boys = 360 (derived from 300).
• Boys left = 390 - 360 = 30.
  • Answer: 30 boys left the school.

Example 4: Dividing Money

• Total amount = 2600 among A, B, and C.
• Condition: 2A = 3B = 4C.

Finding the Ratio

• To find the ratio:
  • Actual ratio: A:B:C = 6:4:3.
• Total parts = 6 + 4 + 3 = 13.

Final Calculation

• 2600 / 13 = 200 (value per part).
• A's share = 6 parts = 6 * 200 = 1200.
  • Answer: A receives 1200.