Understanding percentage changes is a cornerstone of quantitative aptitude for competitive exams like the CAT. This module will equip you with the fundamental concepts and practical applications of percentage increase and decrease, enabling you to solve a wide range of problems efficiently.

A percentage is a fraction of 100. The word 'percent' means 'per hundred'. It's a way to express a number as a fraction of 100, making it easier to compare quantities.

To find the percentage increase, we first calculate the absolute increase (the difference between the new value and the original value). Then, we divide this increase by the original value and multiply by 100.

The formula for percentage increase is:

$\text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$

Similarly, for a percentage decrease, we find the absolute decrease (the difference between the original value and the new value). We then divide this decrease by the original value and multiply by 100.

The formula for percentage decrease is:

$\text{Percentage Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100$

A more efficient way to handle consecutive percentage changes is by using multipliers. An increase of X% means the new value is (100 + X)% of the original, which can be represented by a multiplier of $(1 + X/100)$. A decrease of X% means the new value is (100 - X)% of the original, represented by a multiplier of $(1 - X/100)$.

A common mistake is calculating the second percentage change based on the intermediate value rather than the original value, or vice-versa. Always be mindful of the base value for each percentage calculation. Also, remember that a 20% increase followed by a 20% decrease does not result in the original value.