How to Solve Reverse Percentage Problems (With Examples)

Reverse percentage problems involve working backward to find the original value before a percentage increase or decrease occurred. This is especially useful in finance, shopping, and business analytics.

What Is a Reverse Percentage?

A reverse percentage is when you're given a final value after a percentage change and want to calculate the original value before that change.

Common Situations

Finding the original price before a discount was applied
Working out the pre-tax or pre-inflation amount
Recovering the original value before a percentage increase

Reverse Percentage Formula

After a percentage increase:

Original = Final / (1 + Percentage / 100)

After a percentage decrease:

Original = Final / (1 - Percentage / 100)

Example 1: Price After Discount

A product costs $80 after a 20% discount. What was the original price?

Original = 80 / (1 - 0.20) = 80 / 0.80 = 100

Example 2: Value After Increase

An investment grew by 25% and is now worth $250. What was the original amount?

Original = 250 / (1 + 0.25) = 250 / 1.25 = 200

Tip: Use this formula only when you're certain the percentage change has already been applied to get the final value.

Practice Questions

After a 15% discount, a jacket costs $85. What was the original price?
A price rose by 30% to $195. What was the original price?
A value decreased by 25% to $60. What was it before the decrease?

Answers:

$100
$150
$80

Summary

Reverse percentage problems help you find original values before changes occurred. Depending on whether the final value reflects an increase or a decrease, use the correct formula:

  Increase → Original = Final / (1 + Percentage / 100)
  Decrease → Original = Final / (1 - Percentage / 100)

With a little practice, you'll be able to reverse any percentage change and make smarter financial decisions or solve exam questions with confidence.