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CMAT Topics

Ratio, Proportion

Ratio and proportion help compare quantities and determine relationships between them. Variation explains how one quantity changes when another quantity changes.

Practice MCQs for Ratio, Proportion

Fundamental Principles

Ratio

A ratio compares two quantities of the same kind using division. If a and b are two quantities, their ratio is written as a:b or a/b.

Continued Ratio

When three or more quantities are compared in sequence, it is called a continued ratio. Example: 2:3:5.

Proportion

When two ratios are equal, they are said to be in proportion. If a:b = c:d, then a, b, c and d are in proportion.

Direct Proportion

Two quantities are directly proportional if they increase or decrease together in the same ratio. Example: More workers can complete more work in the same time.

Inverse Proportion

Two quantities are inversely proportional if one increases while the other decreases in the same ratio. Example: More workers require fewer days to complete a fixed amount of work.

Compound Proportion

A proportion involving more than two variables is called a compound proportion. It is commonly used in work, time, distance, and efficiency problems.

Duplicate Ratio

The ratio obtained by squaring both terms of a ratio. If the ratio is a:b, the duplicate ratio is a²:b².

Triplicate Ratio

The ratio obtained by cubing both terms of a ratio. If the ratio is a:b, the triplicate ratio is a³:b³.

Sub-Duplicate Ratio

The ratio of the square roots of the terms of a ratio. If the ratio is a:b, the sub-duplicate ratio is √a:√b.

Sub-Triplicate Ratio

The ratio of the cube roots of the terms of a ratio. If the ratio is a:b, the sub-triplicate ratio is ∛a:∛b.

Essential Formulation Tips

  • Represent ratio terms as multiples of a common variable, such as 3x and 4x.
  • In a proportion, the product of extremes equals the product of means.
  • Check whether quantities move together (direct proportion) or oppositely (inverse proportion).
  • Convert ratios to fractions when cross-multiplication simplifies calculations.

Shortcut Execution Techniques

  • For a:b = c:d, use cross multiplication: ad = bc.
  • In direct proportion, use x₁/y₁ = x₂/y₂.
  • In inverse proportion, use x₁y₁ = x₂y₂.
  • For duplicate and triplicate ratios, simply square or cube both terms.

Contextual Inquiries (FAQs)

Q: What is a compound ratio?

A: The ratio obtained by multiplying the antecedents together and the consequents together. Example: 2:3 and 4:5 give compound ratio 8:15.

Q: How do I identify direct and inverse proportion?

A: If both quantities increase or decrease together, it is direct proportion. If one increases while the other decreases, it is inverse proportion.

Q: What is the difference between ratio and proportion?

A: A ratio compares two quantities, while a proportion states that two ratios are equal.