A number is first increased by 20% and then decreased by 20%. What is the net percentage change in the value of the number?

Introduction / Context:
This question illustrates how successive percentage changes work when the same percentage is used for an increase and then a decrease. Many people wrongly assume that a 20% increase followed by a 20% decrease returns the number to its original value, but this is not true because the base for the second change is different. Understanding this concept is crucial for topics like salary revisions, stock price changes, and compound percentage problems.

Given Data / Assumptions:

• A number is increased by 20% in the first step.
• The resulting value is then decreased by 20% in the second step.
• We are asked to find the overall net percentage change.
• No actual number is given, so we can assume a convenient starting value, such as 100 units, for easy calculation.

Concept / Approach:
The core idea is to represent each percentage change as a multiplication factor. A 20% increase corresponds to multiplying by 1.20. A 20% decrease corresponds to multiplying by 0.80. When these are applied successively, the overall multiplier is the product of the two factors, that is 1.20 * 0.80. From this overall factor, we can determine the final value relative to the original and then express the change as a percentage increase or decrease.

Step-by-Step Solution:
Step 1: Assume the original number is 100 units for simplicity.Step 2: Increase it by 20%: new value = 100 + 20% of 100 = 100 + 20 = 120 units.Step 3: Now decrease this new value by 20%: 20% of 120 = (20/100) * 120 = 24.Step 4: Subtract this from 120: final value = 120 - 24 = 96 units.Step 5: Compare the final value with the original value of 100.Step 6: The change is 96 - 100 = -4 units, meaning a decrease of 4 units.Step 7: Express this as a percentage of the original: (4 / 100) * 100% = 4% decrease.

Verification / Alternative check:
Using multiplication factors, we can write the net effect more compactly. A 20% increase multiplies the number by 1.2, and a 20% decrease multiplies it by 0.8. The combined factor is 1.2 * 0.8 = 0.96. This means the final value is 96% of the original. A value of 96% corresponds to a 4% decrease from 100%. Both this factor method and the numerical example with 100 units give the same conclusion that there is a 4% overall decrease, confirming correctness.

Why Other Options Are Wrong:
Option "increase by 2%" would mean the final value is 102 units when starting from 100, which contradicts the computed 96 units. Option "decrease by 3%" would correspond to a final value of 97 units, again not matching 96. Option "increase by 5%" suggests a final value of 105 units, which is clearly inconsistent. Option "no change" assumes that the effects cancel each other, which is a common misconception. Only a 4% decrease matches the actual calculations.

Common Pitfalls:
Many learners mistakenly think that if you increase and then decrease by the same percentage, the net effect is zero. This happens because they treat percentages additively (20 - 20 = 0) rather than multiplicatively. Another pitfall is to incorrectly apply the second percentage to the original number instead of the increased value. To avoid these issues, always convert each change into a multiplier and apply them one after another to the current value, not the initial value each time.

Final Answer:
The number suffers a net decrease of 4%.