Percentage Change Word Problems
Practice solving percentage change word problems. Enter values, try the problem yourself, then check the step by step answer.
Enter Your Values and Check the Answer
| Step | Working | Value |
|---|
Percentage Change Reference Examples
| Original Value (V1) | New Value (V2) | Change | Result |
|---|---|---|---|
| 100 | 120 | +20 | 20% increase |
| 200 | 150 | −50 | 25% decrease |
| 50 | 75 | +25 | 50% increase |
| 80 | 60 | −20 | 25% decrease |
| 44.90 | 87.80 | +42.90 | 95.55% increase |
| 1200 | 900 | −300 | 25% decrease |
| 5,629 | 5,271 | −358 | 6.36% decrease |
How to Solve Percentage Change Word Problems
Percentage change word problems ask you to find how much a value has changed from one point to another, expressed as a percentage of the original value. These problems appear in math classes, finance, science, and everyday comparisons.
The Percentage Change Formula
V1 is the original or starting value. V2 is the new or ending value. The absolute value of V1 ensures the formula works correctly even with negative starting values.
Steps to Solve Any Percentage Change Problem
- Identify the original value (V1) and the new value (V2) from the problem.
- Subtract V1 from V2 to find the change: V2 − V1.
- Divide the change by the absolute value of V1.
- Multiply by 100 to get the percentage.
- If positive, it is an increase. If negative, it is a decrease.
Worked Examples of Percentage Change
Worked examples of percentage change help you see how the formula applies to different types of problems.
Example 1: Price Change
An item cost $44.90 in 2015 and $87.80 in 2016. What was the percentage change?
(87.80 − 44.90) / 44.90 × 100 = 42.90 / 44.90 × 100 = 95.55% increase
Example 2: Population Change
A town had 5,629 people in 2024 and 5,271 in 2025. What was the percentage change?
(5,271 − 5,629) / 5,629 × 100 = −358 / 5,629 × 100 = 6.36% decrease
When to Use Percentage Change vs Percent Difference
Use percentage change when you have a clear original and new value, meaning the order matters. Use percent difference when comparing two values where neither is clearly the starting point and you only care about the gap between them.
Tips for Percentage Change Word Problems
Tips for solving percentage change word problems help you avoid common mistakes and work faster on tests.
- Always identify which value is V1 (original) and which is V2 (new) before calculating.
- Words like “was” or “last year” point to V1. Words like “is now” or “this year” point to V2.
- A negative result always means a decrease, not a mistake in your work.
- Round to two decimal places unless the problem specifies otherwise.
- Label your answer as an increase or decrease to get full credit on exams.