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Welcome to our Math lesson on Finding the Original Value after a Percentage Change, this is the fourth lesson of our suite of math lessons covering the topic of Percentage Increase and Decrease, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Finding the Original Value after a Percentage Change
If we have the percentage change and the new amount given, we can find the original amount by rearranging the formula
Percentage change = Actual value - Initial value/Initial value × 100%
(If the percentage change is positive, we have a percentage increase involved; otherwise, we have a percentage decrease).
Rearranging the above formula to isolate the original (initial) value, yields
Percentage change = Actual value/Initial value × 100% - Initial value/Initial value × 100%
= Actual value/Initial value × 100% - 100%
Thus,
Actual value/Initial value × 100% = 100% + Percentage change
Initial value = Actual value × 100%/100% + Percentage change
Example 5
The actual price of an item is $270 after a discount of 10%. What was the original price of the item?
Solution 5
We have the actual value = $270 and the percentage change = -10% as the discount involves a percentage decrease. Thus, applying the above formula, yields
Initial value = Actual value × 100%/100% + Percentage change
= $270 × 100%/100% + (-10)%
= $270 × 100%/90%
= $270 × 10/9
= $30 × 10
= $300
We can calculate the original value when we have a percentage increase as well. Let's use another example to illustrate this point.
Example 6
A student obtained 84 points in an exam, increasing her result by 5% compared to the previous exam. What was her previous result?
Solution 6
We have the following clues:
Actual value = 84
Percentage change = +5% (as there is a percentage increase)
Initial value = ?
Using the formula
Initial value = Actual value × 100%/100% + Percentage change
yields
Initial value = 84 × 100%/100% + 5%
= 84 × 100%/105%
= 84 × 20/21
= 4 × 20
= 80 points
More Percentage Increase and Decrease Lessons and Learning Resources
Percentages Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 5.3 | Percentage Increase and Decrease | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 5.3.1 | Percentage Change | | |
| 5.3.2 | Percentage Increase | | |
| 5.3.3 | Percentage Decrease | | |
| 5.3.4 | Finding the Original Value after a Percentage Change | | |
| 5.3.5 | Percentage Distribution | | |
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- Continuing learning percentages - read our next math tutorial: Applications of Percentage in Banking. Simple and Compound Interest
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