Reverse Percentages in Numeracy Aptitude Tests

Many who are asked to complete numerical aptitude test are frequently caught out on reverse percentage questions. In fact, only few follow right steps to work out problems in such questions correctly. In simple terms, reverse percentages are mathematical functions used to solve problems related to finding out unknown quantities after they have increased or decreased. For example, you know that the price of house was £320,000 in 2013 which represented 10% increase from 2012. You would use reverse percentage to find the value of house in 2012. If you are not acquainted or used to these concepts it may be hard to know how to multiply, divide or what operation to take to get to the right answer. In the below tutorial you will find practice examples that will help you to understand how to work out these kinds of problems correctly in your numerical reasoning tests.



How to work out reverse percentage increase

Reverse percentage increase is one of the most important topics to master for your numeracy aptitude tests. It referrers to calculating algebraic functions related to finding value X after it had increased by certain percentage amount. For example, assume that amount X raised by 30% to new figure 70. To find for X you need to apply following formula 70 / (1 + 0.30). To demonstrate this on real test example consider the below question and inspect the figure below.


If the iPhones sales in September rose by 15% from previous month then what was the number of iPhones sold during the August?

As indicated above, to solve this you need to make use of reverse percentage increase that is 200 / (1 + 0.15). However, some test takers that are not acquainted with this method may calculate 200 x (1 – 0.15) which is the incorrect way. Note that this approach rather refers to calculating percentage decrease which is to be applied to situations where you are asked to reduce given amount by certain proportion. Hence, pay attention and read carefully what the question is asking you to do so that you use the correct calculation.


How to work out reverse percentage decrease

When you are required to work out reverse percentage decrease for example to solve for value M that has decreased say by 25% over some period of time to value N which equals to 90 then the formula to use to solve for N would be formulated in following way 90 / (1 – 0.25) = 120. To illustrate this on real example consider the question below.

If the BlackBerry trades went down by 20% from August to September then what was the number of BlackBerry sales in August?

If you inspect the above graph you can see that in September trading company sold 100 BlackBerry iPhones. Hence, you may set up your equation as follows 100 / (1 – 0.20) to calculate sales for August. Fairly simple isn’t it.

In your numerical reasoning test the faster and quicker way to calculate the above is to mentally subtract given percentage, in the above case 0.20 from 1, and only perform calculation of 100 / 0.80 on your calculator. Similarly, for reverse percentage increase add together in your head 1 and 0.20 and then calculate on your calculator only 100 / 1.20. Remember, time is precious in numerical reasoning tests and hence attempt to make as many calculations in your head as possible.