Reverse Percentages

Reverse percentages, also known as backwards percentages, involve finding the original amount when you know the final amount after a percentage increase or decrease.

Here's how you can calculate it:

Percent Increase:

If you know the percentage by which an amount has increased and the final amount, you can find the original amount by dividing the final amount by 1 plus the percentage increase as a decimal.
Formula: Original Amount = Final Amount / (1 + (Percentage Increase / 100))
Percent Decrease:

Similarly, if you know the percentage by which an amount has decreased and the final amount, you can find the original amount by dividing the final amount by 1 minus the percentage decrease as a decimal.
Formula: Original Amount = Final Amount / (1 - (Percentage Decrease / 100))

Example 1: Percent Increase
Suppose an item increased by 20% and now costs $120. You want to find out its original price.

Original Amount = Final Amount / (1 + (Percentage Increase / 100))
Original Amount = 120 / (1 + (20 / 100))
Original Amount = 120 / (1 + 0.20)
Original Amount = 120 / 1.20
Original Amount = $100

So, the original price of the item was $100.

Example 2: Percent Decrease
Suppose an item decreased by 25% and now costs $60. You want to find out its original price.

Original Amount = Final Amount / (1 - (Percentage Decrease / 100))
Original Amount = 60 / (1 - (25 / 100))
Original Amount = 60 / (1 - 0.25)
Original Amount = 60 / 0.75
Original Amount = $80

So, the original price of the item was $80.

These formulas should help you calculate the original amount when you know the final amount and the percentage change.