# 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.

## Calculating Reverse Percentages

• 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.

## Common Mistakes to Avoid

• 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%.

## Real World Applications of Reverse Percentages

• 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.