Reverse Percentages

Understanding Reverse Percentages

Reverse percentages are a way of working backwards on percentage problems.
The concept of reverse percentages is used for finding the original quantity before a percentage increase or decrease.
These are often applied in problems involving sales, discounts, tax increases, or population growth and decline.

A common method for reverse percentage problems is to represent the problem algebraically and then solve for the original quantity.
Consider the final amount as 100% and adjust the percentage accordingly. If there was a 20% increase, the original amount is 100% - 20% = 80% of the final amount.
To find the original amount after an increase, divide the final value by 1 plus the rate of increase. For example, if a price increased by 15% to a final price of £115, the original price would be 115 ÷ 1.15 = £100.
To find the original amount after a decrease, divide the final value by 1 minus the rate of decrease. For example, if a value decreased by 30% to a final value of 70, the original value would be 70 ÷ 0.70 = £100.

Remember to convert the percentage to a decimal before calculations. For instance, 15% should be used as 0.15 in calculations.
Avoid assuming the original quantity is 100% and then adding or subtracting. You have to consider that percentage increases or decreases change the base for quantifying 100%.

Knowledge of reverse percentages is very beneficial in financial context. For example, knowing how much you originally paid for an item that is now on sale.
Reverse percentages can be applied in calculations of profit and loss, as well as other business and financial transactions.
This concept can also be used to check expected returns on investments or the effectiveness of discounts and offer schemes.