# 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

1. Following a $$20\%$$ increase in price, a pair of shoes costs $$\ \ 96$$. How much did the shoes cost before their price was increased?

2. Following a $$25\%$$ decrease in price, Clara's gym class cost $$\ \ 90$$. How much did her gym class used to cost?

3. 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?

4. 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?

5. 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?

6. 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?

7. 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.

8. 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.

Note: this exercise can be downloaded as a worksheet to practice with:

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