Basic Concepts of Ratio and Proportion

Before solving ratio and proportion questions, remember these simple points:

1. Ratio Formula:
   Ratio = Quantity₁ : Quantity₂ = Quantity₁ / Quantity₂
   (It shows how many times one number contains another.)

2. Proportion Formula:
   If two ratios are equal, they form a proportion.
   Example: a : b = c : d → a/b = c/d

3. Finding One Quantity from a Ratio:
   If total = T and ratio parts = a : b : c,
   Each share = (individual part ÷ total parts) × T

4. Shortcut for Ages and Investments:

   • For age problems: Use variables like 6x, 7x for ratio parts.

   • For partnership/investment: Multiply investment × time to get ratio.

5. Percentage Relation to Ratio:
   If one value is X% more or less than another, convert it to ratio form.
   Example: 20% more → 120 : 100 = 6 : 5

These basics are enough to solve all ratio and proportion questions easily.

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