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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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