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Aptitude Topics

Age Ratios

Ratio problems are the most common type of age problem. By treating ages as 'units' of a total value, you can often bypass heavy algebra in favor of simple ratio arithmetic.

Fundamental Principles

Ratio Units

A way to express ages as parts of a whole (e.g., $3x$ and $4x$). The difference between ratio units must correspond directly to the difference in real-world years.

Essential Formulation Tips

  • If the ratio of two people's ages is $a:b$, always represent their ages as $ax$ and $bx$.
  • Never add the years directly to the ratio units *before* solving for $x$. You must add the years to the *value* of the units.

Shortcut Execution Techniques

  • The Cross-Difference Shortcut: For a ratio changing from $a:b$ to $c:d$ over $t$ years, the unit value $x$ can be found using the cross-multiplication difference: $x = \frac{t \times |c - d|}{|ad - bc|}$.

Contextual Inquiries (FAQs)

Q: Why does the ratio change over time?

A: Because the same number of years added to both ages represents a smaller percentage increase for the older person and a larger percentage increase for the younger person.