A percentage change question is asking you to calculate the difference between two numbers and present it as a percentage. This is a very common type of question found in numerical reasoning tests, so it’s important to make sure you understand what’s asked and memorise the relevant formulas.
Being able to calculate a percentage change is a skill used a lot in everyday life – for example, working out a service tip on a bill, or a price reduction on a sale item. Understanding and being able to calculate percentage changes easily is an advantageous ability for many jobs, since it shows you can interpret numerical data.
How to easily calculate percentage change
Even if you are given a numerical reasoning test without a calculator, working out percentage changes is straightforward once you know the formulas.
- Increase: (B - A) / A x 100
- Decrease: (A - B) / A x 100
A represents your starting number and B represents the new value.
Remember to only use the % function on your calculator if you are familiar with how it works; otherwise you may end up making errors that you are unable to correct.
By learning the formulas, you will always know the steps needed to make the right calculations and you can check the working out.
Example percentage change question 1
Here is an example demonstrating the formula above for a percentage increase:
You have £150 in your savings account. You are given £35 for your birthday. What is the increase as a percentage?
Formula: (B - A) / A x 100
A = 150
B = (150 + 35) = 185
(185 - 150) / 150 x 100
35 / 150 x 100
0.23 x 100
Percentage increase = 23%
Example percentage change question 2
Here is a similar question, this time looking at a percentage decrease:
You have £150 in your savings account. You spend £67. What is the decrease as a percentage?
Formula: (A - B) / A x 100
A = 150
B = (150 - 67) = 83
(150 - 83) / 150 x 100
67 / 150 x 100
0.45 x 100
Percentage decrease = 45%
Example percentage change question 3
Another kind of percentage question is working back from a percentage, otherwise known as a reverse percentage question. Here is an example showing how you would work this out:
You buy a dress that is 40% off for £50. What was the original price?
Formula: (A / B) = Original value
A = Present value = £50
B = Relation to original value as a decimal = 0.6
50 / 0.6 = 83.33
If the percentage increases, your decimal will be over 1 as it presents more than 100% of the original value. For example:
You sold your clock in 2020 for £200; this was a 70% increase in value. How much was the original price?
A = 200
B = 1.7
200 / 1.7 = 117.65
Tips for working out percentage change accurately
Don’t rely on your calculator
It may come as a surprise, but it is often quicker to do percentage calculations mentally, so even if you’re allowed one in your test, you should aim to memorise the formulas anyway. This will also help you check your answers – if you’ve made a mistake with your calculator functions then you’ll catch the error by doing it mentally.
Don’t forget to adjust the base number
If X is reduced by 20% this equals Y. Therefore, further changes should be applied to Y, not to the original X. Often this will be given as year-on-year changes in a question, so remember to read the question carefully to understand the terms of the percentage change.
Check the instructions carefully
Particularly when the test asks for your answers to be rounded, e.g. to the nearest whole number or to two decimal places. This is a simple error that catches a lot of people out.
Write down your calculations
This allows you to check your numbers and more easily spot errors.