Reverse Percentage: Formula, Methods and Examples
Reverse Percentage is used to find the original value when the final value and percentage change are known. The original value is found by dividing the final value by the remaining percentage multiplier after an increase or decrease. This page covers the reverse percentage formula, calculation methods, shortcuts, and solved numerical examples.
What Is Reverse Percentage?
After a p% increase, the final value is (100 + p)% of the original value. After a p% decrease, it is (100 - p)% of the original value. Therefore, the original value is found by dividing the final value by the relevant multiplier. For example, if a value becomes 120 after a 20% increase, the original value is 120 ÷ 1.20 = 100.
Reverse Percentage Formula & Tricks
Important Formulas
Use this formula when the final value is obtained after increasing the original value by p%.
Use this formula when the final value is obtained after decreasing the original value by p%.
If a given amount represents p% of the original value, divide that amount by p/100.
Quick Tricks
For an increase of p%, divide the final value by (100 + p)/100. For a decrease of p%, divide it by (100 - p)/100. This avoids calculating the percentage change separately.
A p% increase makes the final value (100 + p)% of the original, while a p% decrease makes it (100 - p)%. Use the ratio final value : original value to reverse the change.
Reverse Percentage Concepts
Reverse Percentage After an Increase
An increase of p% changes the original value into (100 + p)% of itself. The final-to-original ratio is (100 + p):100. Hence, divide the final value by (100 + p)/100.
Reverse Percentage After a Decrease
A decrease of p% leaves (100 - p)% of the original value. The final-to-original ratio is (100 - p):100, so the final value must be divided by (100 - p)/100.
Finding the Original Value from a Percentage Amount
This case does not involve a final changed value. It directly uses the relation A = p/100 × original value. Rearranging this equation gives the original value.
Reverse Percentage in Successive Changes
An increase of a% followed by a decrease of b% gives the final multiplier (1 + a/100)(1 - b/100). Thus, original value = final value ÷ [(1 + a/100)(1 - b/100)]. The order of multiplication does not affect the product.
Reverse Percentage Video Lessons
Watch short topic-wise lessons for quick revision.
Percentage Data Comparison and Reverse Problems
Learn to compare percentage-based data and solve reverse percentage problems by working backward from a given value to determine the original quantity.
Practice Reverse Percentage Questions
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Reverse Percentage Quick Quiz
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Reverse Percentage Revision Points
Use the correct final-value multiplier to calculate the original value.
- After a p% increase, final value = original value × (100 + p)/100.
- After a p% decrease, final value = original value × (100 - p)/100.
- Original value after an increase = final value × 100/(100 + p).
- Original value after a decrease = final value × 100/(100 - p).
- If A is p% of a number, the number = A × 100/p.
- For successive changes, multiply all change factors before reversing the result.
- A percentage decrease and the same percentage increase do not cancel each other; their multipliers are different.
Reverse Percentage FAQs
What is the reverse percentage formula after a 20% increase?
Original value = Final value × 100/120, or Final value ÷ 1.20. For example, if the final value is 600, the original value is 600 × 100/120 = 500.
What is the reverse percentage formula after a 20% decrease?
Original value = Final value × 100/80, or Final value ÷ 0.80. If the final value is 640, the original value is 640 × 100/80 = 800.
A number becomes 840 after a 40% increase. What was the original number?
An increase of 40% makes the final value 140% of the original. Original number = 840 × 100/140 = 600.
A price falls to ₹1,500 after a 25% reduction. What was its original price?
After a 25% reduction, the final price is 75% of the original. Original price = 1,500 × 100/75 = ₹2,000.
If 30% of a number is ninety, what is the number?
Number = 90 × 100/30 = 300. Here, 90 is the given percentage amount, not the final value after a percentage change.
Can the same percentage increase and decrease restore the original value?
No. A p% increase followed by a p% decrease gives the multiplier (1 + p/100)(1 - p/100) = 1 - p²/10,000, which is less than 1 for p greater than zero. For example, increasing 100 by 20% and decreasing it by 20% gives 96.