Lesson 2.3: Ratio, Proportion & Percentage

Objective: Understand ratio, proportion, and percentage concepts, and learn quick calculation techniques for Banking Exams.

1. Ratio Basics

• Definition: Ratio compares two quantities of the same kind.

  • Example: If there are 10 boys and 15 girls, ratio of boys to girls = 10:15 = 2:3

• Simplification: Divide both numbers by their HCF.

• Applications: Mix problems, profit sharing, ingredient mixtures, population ratios.

2. Proportion

• Definition: Proportion states that two ratios are equal.

  • Example: If 2/3 = x/9, then x = 6

• Rule: Cross-multiply to find the unknown.

3. Percentage

• Definition: A fraction with denominator 100.

  • Formula: Percentage = (Part ÷ Whole) × 100

  • Example: A student scored 45 out of 60 → Percentage = (45 ÷ 60) × 100 = 75%

• Increase & Decrease:

  • Increase % = (Increase ÷ Original) × 100

  • Decrease % = (Decrease ÷ Original) × 100

• Conversion:

  • Ratio → Percentage: ab×100\frac{a}{b} × 100ba​×100

  • Percentage → Ratio: Convert % to fraction and simplify

4. Shortcut Tricks

1. Direct Proportion Shortcut: a:b = c:d → Cross multiply: a×d = b×c

2. Percentage Tricks:

   • 10% of a number = Divide by 10

   • 5% of a number = 10% ÷ 2

   • 25% of a number = 1/4 of the number

3. Quick Ratio Calculation: For sharing profit/loss:

   • Share of A = A’s part ÷ Total parts × Total profit/loss

5. Tips for Banking Exams

• Memorize common percentage values (10%, 20%, 25%, 50%, 75%).

• Practice ratio-based word problems like mixtures, ages, and investments.

• Solve shortcut calculations daily to increase speed.

• Always simplify ratios before using in proportion problems.

✅ Lesson Summary:
Mastering Ratio, Proportion, and Percentage is essential for solving Banking Exam questions quickly. Use shortcut methods and practice word problems for better accuracy and speed.