Successive percentage changes are a fundamental concept in quantitative aptitude, frequently tested in competitive exams like the CAT. Understanding how to efficiently calculate the net effect of multiple percentage changes is crucial for saving time and ensuring accuracy. This module will break down the concept, provide practical methods, and equip you with the skills to tackle these problems confidently.

Successive percentage changes occur when a percentage change is applied to a value, and then another percentage change is applied to the new value. It's important to note that the second (and subsequent) percentage change is calculated on the result of the previous change, not the original value. This is a common pitfall if not understood correctly.

This method involves calculating each percentage change sequentially. While straightforward, it can be time-consuming for multiple changes.

Example: A salary of ₹10,000 is increased by 20% and then by 10%.

1. Increase by 20%: ₹10,000 + (20% of ₹10,000) = ₹10,000 + ₹2,000 = ₹12,000.
2. Increase by 10% on the new amount: ₹12,000 + (10% of ₹12,000) = ₹12,000 + ₹1,200 = ₹13,200. The final salary is ₹13,200.

This is a more efficient method. Each percentage change can be represented by a multiplier. An increase of X% is equivalent to multiplying by (1 + X/100), and a decrease of Y% is equivalent to multiplying by (1 - Y/100).

Example (using the same salary scenario): A salary of ₹10,000 is increased by 20% and then by 10%. Multiplier for 20% increase = (1 + 20/100) = 1.20. Multiplier for 10% increase = (1 + 10/100) = 1.10. Final Salary = Original Salary × Multiplier1 × Multiplier2 Final Salary = ₹10,000 × 1.20 × 1.10 = ₹10,000 × 1.32 = ₹13,200.

For two successive percentage changes, say an increase of 'a%' and then a decrease of 'b%', the net percentage change can be calculated using the formula: Net Change % = (a - b - ab/100)%. If both are increases, it's (a + b + ab/100)%. If both are decreases, it's (-a - b + ab/100)%.

Example: A price is increased by 20% and then decreased by 10%. Here, a = 20 (increase) and b = 10 (decrease). Net Change % = (20 - 10 - (20 * 10)/100)% Net Change % = (10 - 200/100)% Net Change % = (10 - 2)% Net Change % = 8%. This means there is a net increase of 8%.

For more than two successive changes, the multiplier method (Method 2) is generally the most efficient and least error-prone. Simply multiply the original value by the respective multipliers for each change.

Example: A value is increased by 10%, then decreased by 20%, and finally increased by 30%. Multiplier 1 (10% increase): 1.10 Multiplier 2 (20% decrease): 0.80 Multiplier 3 (30% increase): 1.30 Net effect = 1.10 * 0.80 * 1.30 = 0.88 * 1.30 = 1.144. This represents a net increase of 14.4%.

1. Base Value: Always ensure you are applying the percentage to the correct base value (the result of the previous change, not the original). The multiplier method inherently handles this.
2. Increases vs. Decreases: Be meticulous with signs. Increases use multipliers > 1, decreases use multipliers < 1.
3. Net Change vs. Final Value: Understand whether the question asks for the net percentage change or the final value itself.
4. Practice: The more you practice, the more intuitive these calculations become.