What Is a Reverse Percentage and How to Calculate It?
Application tests are becoming more and more commonplace for job seekers these days, particularly for jobs that require mathematical reasoning.
Whether you’ve applied for a job in sales, marketing, accounting, or any other gig that requires an in-depth knowledge of reverse percentages, avoid panicking and being caught off-guard by preparing ahead of time.
The following informational guide is a crash course on reverse percentages. Discover everything from an overview of this computation that is necessary for various fields and industries to step-by-step instructions that will teach you how to successfully solve reverse percentages.
After reading the information presented below, you’ll be ready to ace a numerical reasoning test and land whatever gig you’ve applied for.
Table of Contents
What Is a Reverse Percentage?
A reverse percentage (also referred to as an inverse percentage) is a mathematical computation that is used to find the original amount, price, or value of something after that something has been given a percentage discount or an increase has been applied.
In order to determine the original amount of a given percentage, you have to work backwards.
Reverse percentages are commonly found in numerical reasoning tests to determine a job seeker’s basic understanding of numbers, data, and mathematics. This computation can also be beneficial in other types of aptitude tests, such as mechanical reasoning.
In any position that requires figuring out what the original amount of something was after it has already been discounted with a percent, understanding how to calculate reverse percentages is necessary.
Having a firm understanding of this mathematical computation is also important for everyday life, such as when you’re grocery shopping, paying bills, or budgeting expenses.
Reverse percentages can be determined using a calculator or long-hand without a calculator.
How to Calculate Reverse Percentages Using a Calculator
To find the original amount of a specific percentage of the amount using a calculator, use the following steps:
- Write down the given percentage and make it equal to the amount that you’ve been given.
- Divide both sides by the percentage. For example, if you have 70 percent, divide both sides by 70. Doing so will give you 1 percent.
- Multiply both sides by 100, which will give you 100 percent.
Example Questions and Calculations Using a Calculator
Question 1: What is the original number if 45 percent of a number is 36?
- Make the percentage equal to the amount: 45 percent = 36
- In order to find 1 percent, divide both sides by the percentage. To illustrate, if 45 percent = 46, divide 45 percent by 45, which equals 1, and divide 36 by 45, which equals 0.8. Therefore, 1 percent = 0.8
- To find 100 percent, multiply by 100. To illustrate, if 1 percent = 0.8, multiply 1 percent by 100, which equals 100 percent, and multiply 0.8 by 100, which equals 80.
Answer: the original number was 80
Question 2: If 150 percent of a number is 690, what is the original number?
- Make the percentage equal to the amount: 150 percent = 690
- To find 1 percent, divide both sides of the above by the percentage. In this example, the percentage is 150, so you’d divide both sides of the above by 150. To illustrate, 150 percent divided by 150 = 1 percent and 690 divided by 150 = 4.6.
- To find 100 percent (the original amount), multiply by 100. To illustrate, if 1 percent = 4.6, multiply 1 percent by 100, which equals 100 percent, and multiply 4.6 by 100, which equals 460.
Answer: If 150 percent of a number is 690, the original number was 460.
How to Calculate Reverse Percentages Without a Calculator
If you find that you need to figure out a reverse percentage and you don’t have a calculator handy or you aren’t permitted to use one, you can use basic mental math to complete the calculation.
Typically, common factors can be used to simplify the problem. In other words, instead of finding 1 percent, which could require complex division, you could find 10 percent, 25 percent, or any other percentage that is a factor of 100 percent.
Use the following steps to mentally calculate reverse percentages:
- Write down the percentage and make it equal to whatever amount you’ve been given.
- Find a common factor of the percentages and 100 percent. A common factor is a number that goes into both numbers.
- In order to determine the percentage of your amount, divide.
- To find 100 percent, multiply.
Example Questions and Calculations without a Calculator
Question 1: If 70 percent of a given amount is 56, what is the original amount?
- Make the percentage equal to the amount, so 70 percent = 56
- Identify a common factor of 70 percent and 100 percent. Common factors include 1,2,5, 10
- While you can use any of the common factors, it’s best to use the common factor that allows for the easiest calculation, which is typically the highest common factor. In this example, we’ll use 10 percent.
- Because 10 percent is a factor of both 70 percent and 100 percent, you have to find 10 percent of the amount. In order to do this, you will need to divide by 7, since 70 percent divided by 7 = 10 percent. To illustrate, 70 percent divided by 7 = 10 percent and 56 divided by 7 = 8.
- Once you have 10 percent, to find 100 percent, you will need to multiply by 10. To illustrate, 10 percent = 8, so 10 percent multiplied by 10 = 100 percent and 8 multiplied by 10 = 80
Answer: The original amount was 80.
It’s important to note that for the above-mentioned example, as well as every other example, the method of finding the percentage could also be used. We decided to find 10 percent in this example and not 10 percent because it’s easier to calculate 56 divided by 7 mentally or without a calculator.
Question 2: If 125 percent of a number is 350, what is the original value?
- Make the percentage equal to the amount, so 125 percent = 350
- Identify a common factor of 125 percent and 100 percent, which include 2 and 25
– While either number would work, we’ve decided on 25, as it’s easier to work with.
- Since 25 is a factor of both 125 percent and 100 percent, you have to figure out 25 percent of the amount. In order to do this, you need to divide by 5, because 125 percent divided by 5 = 25 percent. To illustrate, 125 percent divided by 5 = 25 and 350 divided by 5 = 70
- Since you now have 25 percent, you need to multiply by 4 in order to find 100 percent. To illustrate, 25 percent multiplied by 4 = 100 percent and 70 multiplied by 4 = 280.
Answer: The original amount was 280.
Key Factors to Keep In Mind When Calculating Reverse Percentages
- The easiest way to calculate a reverse percentage is by working from whatever the value of 100 percent is.
- An easy way to recall how to find the percentage of a value is by using this basic equation: value/100 x percentage.
- If you’re having a difficult time trying to calculate a challenging reverse percentage, breaking down a value into its 1 percent, 10 percent, or 25 percent form can help, as calculating these values mentally tends to be easier. Therefore, it can provide you with an alternate point to start at.
- While a calculator will make things easier, you may not always have one on hand or may not be permitted to use one. As such, knowing how to calculate reverse percentages mentally is very important.
Using Reverse Percentages Given a Specific Percentage Increase or Decrease
In some instances, rather than being given a specific percentage of an amount, you will be told the percentage increase or decrease that has taken place.
When comparing the calculations that have already been discussed, the only difference is that you will first need to determine what percentage of the original amount you now have.
You can do this using the following steps:
- Determine what percentage of the original amount you now have. If it has increased by a percentage, add that percentage to 100 percent. If it has been decreased by a percentage, subtract that percentage from 100 percent.
- Write down the percentage so that it is equal to the given amount.
- You can then use either the calculator method or the non-calculator mental method described above in order to find 100 percent.
Example Questions and Calculations Using a Calculator
Question: The number of fans at this week’s baseball game was 12 percent more than the previous week. If 728 fans attended this week’s game, how many fans attended the previous week?
- The percentage increase is 12 percent, so 100 percent + 12 percent = 112 percent
- Make the percentage equal to the given amount: 112 percent = 728
- To find 1 percent, divide 112 percent and 728 by 112, which equates to 1 percent = 6.5, then multiply 1 percent and 6.5 by 100, which equals 650.
Answer: There were 650 fans at last week’s game.
What Is a Percentage?
Need to go back to the basics before tackling reverse percentages? Let’s remember what a percent is.
A percentage is defined as a part of a whole that is expressed in hundredths; a ratio or number that is expressed as a fraction of 100.
When broken down, the word “percent” literally means “per 100”. In order to calculate the percent of a number, you need to divide the number by the whole and then multiply by 100.
The word “percent” or the “%” symbol is used to represent the result of the calculation, which can further be represented as a simple fraction or decimal fractions.
To illustrate, 1 percent or 1% is a hundredth and 100 percent or 100% represents the whole. For instance, 1 percent of 1,000 crayons equals 1/100 of 1,000 or 10 crayons.
The most effective way is to take practice tests. We highly recommend the resources at Job Test Prep that give you real-life simulation questions on reverse percentages and many other numerical reasoning topics.
Sarah is an accomplished educator, researcher and author in the field of testing and assessment. She has worked with various educational institutions and organisations to develop innovative evaluation methods and enhance student learning. Sarah has published numerous articles and books on assessment and learning. Her passion for promoting equity and fairness in the education system fuels her commitment to sharing insights and best practices with educators and policymakers around the world.