Welcome to this module focused on a crucial area of quantitative aptitude: Percentage Change in Products and Ratios. This topic is fundamental for many competitive exams, including the CAT, and understanding it deeply will equip you to solve a wide range of problems efficiently.

When the price or quantity of a product changes by a certain percentage, it affects the total revenue or cost. This concept is often tested in problems involving price, consumption, and expenditure. The core idea is to understand how successive percentage changes compound.

Let's apply this to a practical scenario. If the price of a product increases by 10% and then decreases by 10%, the net change is not zero. Using the formula: Net Change % = 10 + (-10) + (10 * -10 / 100) = 0 - 100/100 = -1%. So, there's a net decrease of 1%.

Ratios represent a comparison between two or more quantities. When these quantities change, the ratio between them also changes. Understanding how percentage changes in individual components affect the ratio is key.

Many problems combine these concepts. For instance, if the price of a commodity increases by a certain percentage, and its consumption decreases by another percentage, the total expenditure (Price × Consumption) will change. This change in expenditure can be calculated using successive percentage change principles. Similarly, if the ratio of two quantities changes due to percentage variations in them, you might be asked to find the new ratio or the percentage change in the ratio itself.

To excel in this area, focus on:

1. Understanding the core formulas: Especially the successive percentage change formula.
2. Visualizing the impact: Think about how changes affect the whole.
3. Practicing diverse problems: Work through examples involving price, consumption, revenue, and ratio manipulations.
4. Breaking down complex problems: Identify the individual percentage changes and ratio components.