How to Calculate Reverse Percentages
(Reverse Percentage Increases & Decreases)
We're faced with a Reverse Percentage problem as soon as we are given the value of a number following either a percentage increase or a percentage decrease and we're asked to find what the number was, its initial value, before the increase (or decrease) took place.
Here's a typical reverse percentage question:
Due to high demand, a pair of shoes' price was increased by \(20\%\) and they now cost \(\$ \ 96\). How much did the shoes cost before their price was increased?
Reverse Percentage Increase or Decrease?
The example, above, is a typical reverse percentage increase question. Had the price of the pair of shoes been decreased by \(20\% \) it would have been a reverse percentage increase question.
In the following two tutorials we learn how to solve such problems. Watch them before trying to work through the questions further down.
Tutorial 1: Reverse Percentage Increase
In the following tutorial we work through an example in which we solve a reverse percentage increase problem.
Tutorial 2: Reverse Percentage Decrease
In the following tutorial we work through an example in which we solve a reverse percentage decrease problem.
Exercise 1
- Following a \(20\%\) increase in price, a pair of shoes costs \(\$ \ 96\). How much did the shoes cost before their price was increased?
- Following a \(25\% \) decrease in price, Clara's gym class cost \(\$ \ 90\). How much did her gym class used to cost?
- A few years ago Cathy decided to invest in property and bought an apartment. She has been very fortunate and its value has gone up by \(24\%\) and is now worth \(\$ \ 198\ 400\). How much was Cathy's apartment worth when she bought it?
- A clothes shop puts everything on sale with a \(30\%\) discount. After looking around for a while, Charlotte buys a dress for \(\$ \ 84\). How much would she have had to pay if there hadn't been a discount?
- Next month, the price of Benjamin's monthly bus ticket will increase by \(6\%\) and will cost \(\$ \ 42.40\). How much does Benjamin's ticket currently cost?
- Following a low sugar diet, as well as regular exercise, John reduced his weight by \(8\% \) and now weighs \(72\) kg. Rounding your answer to the nearest kg, how much did John weigh before his diet?
- Last fall, a highly selective university offered \(6\% \) of its applicants a place. Given that the university accepted \(540\) students, find how many students applied.
- From grade 8 to grade 9, the number of hours spent studying at home is expected to increase by \(30\%\) to \(14\) hours a week. Rounding your answer to the nearest hour, find how many hours per week students are expected to study in grade 8.
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