Reverse percentages
Understanding Reverse Percentages
- A Reverse percentage problem involves finding the original amount before a change occurred with the knowledge of the changed amount and the percentage change.
- These problems often arise in contexts such as reductions in price, population changes, or increases in income.
- It requires a good understanding of the concepts related to percentages, including percentage increase and decrease.
Calculating Reverse Percentages
- To find the original price before a percentage decrease, you need to divide the final cost by the fraction that remains after the reduction. For example, if the price was reduced by 20%, you should divide the final cost by 0.8 ( because 100% - 20% = 80% or 0.8 in decimal form).
- If there was a percentage increase, divide the final amount by the fraction that represents the increased value. For example, if the population increased by 15%, divide the final population by 1.15 (because 100% + 15% = 115% or 1.15 in decimal form).
Example of Calculating Reverse Percentages
- To demonstrate, suppose an item on sale costs £80 after a 20% discount. The original price can be calculated by dividing £80 by 0.8 (the fraction after a 20% decrease), which totals to £100.
Practical Application of Reverse Percentages
- Understanding reverse percentages is essential for financial planning, budgeting, and market analysis.
- It helps when calculating original prices after discounts, determining original quantities before percentage increases and computing adjusted values when conditions revert to original.
Checking Your Work
- It’s crucial to review and verify your answers to ensure they’re accurate.
- After you calculate the original amount using reverse percentages, apply the percentage decrease or increase to your calculated original amount. Your calculated final value should match the initial final value given in the problem. If it doesn’t, you may need to revise your calculations.
Common Mistakes to Avoid
- When dealing with reverse percentages, it’s a common error to apply the percentage change to the final amount again rather than working out the original value. Be careful to correctly interpret what the question is asking for.
- Ensure that percentage decreases/increases are represented as fractions correctly. A decrease by 20% should be represented as 0.8 and an increase by 15% as 1.15. Using incorrect values will lead to incorrect answers.