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Aptitude Topics

Proportion

A proportion is a statement or equation showing that two ratios are equal to one another.

Fundamental Principles

Proportion Rule

If a : b = c : d, then the four quantities a, b, c, and d are in proportion. This is written as a : b :: c : d. The outer terms 'a' and 'd' are called extremes, and the inner terms 'b' and 'c' are called means.

Mean Proportion

The mean proportion between two numbers 'a' and 'b' is the square root of their product, calculated as √(a * b).

Essential Formulation Tips

  • Product of Extremes = Product of Means. For a : b :: c : d, this means a * d = b * c.
  • If three numbers a, b, and c are in a continuous proportion (a : b :: b : c), then b² = a * c.

Shortcut Execution Techniques

  • Fourth Proportion Shortcut: To find the missing fourth term 'd' in a : b :: c : d, calculate it directly as d = (b * c) / a.

Contextual Inquiries (FAQs)

Q: What is the difference between a ratio and a proportion?

A: A ratio compares two specific values, while a proportion is an equation that sets two ratios equal to each other.