Reverse percentages are a mathematical concept that involves working backwards from a final value with the aim of finding the starting or original value before an increase or decrease occurred. This concept is commonly used in accounting, determining discounts and taxes, or solving other real-life situations that involve percentage changes. In this article, we will describe a step-by-step approach to tackle reverse percentage calculations with ease.

Step 1: Understand the problem

Before diving into calculations, take a moment to read and understand the problem carefully. The problem usually gives you the amount after an increase or decrease and requires you to find the original amount.

Step 2: Define variables

Assign symbols for each of the known and unknown variables. Here’s a common notation:

– O: Original value (the starting value)

– P: Percentage (increase or decrease)

– N: New value (value after the increase or decrease)

The problem may require you to solve for O, given P and N.

Step 3: Use the percentage change formula

Express the relationship between these variables using the standard percentage change formula:

N = O + (O × P)

For example, if there is a 20% increase in cost, then P = 0.2. If it’s a decrease, represent it as a negative number (e.g., P = -0.2 for a 20% decrease).

Step 4: Rearrange for O

As our objective is to find ‘O,’ we should now rearrange the formula accordingly:

O + (O × P) = N

O (1 + P) = N

O = N / (1 + P)

Step 5: Plug in values and calculate

Insert values for N and P from the given problem into the rearranged formula to calculate ‘O’:

O = N / (1 + P)

For example, let’s say a product now costs $120 after a 20% increase. We need to find its original price.

P = 0.2 (20% increase)

N = 120

Plug these values into the formula:

O = 120 / (1 + 0.2)

O = 120 / 1.2

O = 100

The original price of the product was $100.

Conclusion

Reverse percentage calculations are a valuable tool for solving numerous everyday problems. By following these steps—understanding the problem, defining variables, using the percentage change formula, rearranging it, and plugging in values—you can effortlessly determine the original value before an increase or decrease. Keep practicing to sharpen your skills and conquer reverse percentage calculations in various scenarios.