How to calculate a percentage increase

Welcome to this article on exercises on business calculations and more specifically on how to calculate a percentage increase. Here you will find questions and answers related to the subject. But also no less than 9 detailed corrected management exercises on business calculations for Operational Management.

By the end of this article, you will know how to calculate a percentage increase in business calculations without any worries. If you wish, do not hesitate to go directly to the 9 corrected exercises in order to train you.

Introduction

Percentage increase is a commonly used concept in various fields such as finance, statistics, business, and even in everyday life. Whether you want to calculate your salary increase, the price of a product increase, or the number of users of your website increase, understanding how to calculate a percentage increase is an essential skill.

The importance of knowing how to calculate a percentage increase lies in its ability to provide a clear and accurate picture of how a value has changed over time. It is a powerful tool that can help you make informed decisions, whether you are managing your personal budget, evaluating the performance of an investment, or analyzing market trends.

However, while the concept may seem simple, calculating a percentage increase can sometimes be confusing, especially if you're not familiar with math. That's why we've created this comprehensive guide to help you understand and master this calculation.

In this guide, we will define what a percentage increase is, explain how it is calculated, and walk you through the steps to perform the calculation. We will also provide real-world examples to illustrate the process and answer the most frequently asked questions on this topic. So, whether you are a student, a professional, or simply someone who wants to improve their math skills, this guide is for you.

What is a percentage increase?

Before diving into the calculation process, it is important to understand what a percentage increase is. In simple terms, a percentage increase is a measurement that indicates how much a value has increased in proportion to its initial value. It is usually expressed as a percentage, hence the name.

For example, if the price of a product increases from 100 euros to 120 euros, we can say that it has increased by 20%. Similarly, if your salary increases from 2 euros to 000 euros, it has increased by 2%. In these examples, the percentage increase gives a clear idea of ​​the magnitude of the increase compared to the initial value.

It is important to note that percentage increase is different from absolute increase. Absolute increase is simply the difference between the final value and the initial value. In the product example, the absolute increase is $20 ($120 – $100), while percentage increase is 20%. So percentage increase is a relative measure that takes into account the initial value, while absolute increase is an absolute measure that does not take into account the initial value.

Understanding this distinction is essential to correctly interpreting percentage increases. For example, a €50 increase may seem significant, but if the initial value was €1, the percentage increase is only 000%, which is not that significant. On the other hand, a €5 increase on an initial value of €50 is a percentage increase of 100%, which is much more significant.

How the percentage increase calculation works

Now that we have a clear understanding of what a percentage increase is, it is time to understand how it is calculated. The calculation of the percentage increase is based on a simple mathematical formula.

The formula for calculating a percentage increase is:

Percentage Increase = (Final Value – Initial Value) ÷ Initial Value x 100

This formula may seem a little intimidating if you're not familiar with math, but it's actually quite simple to understand.

The first part of the formula, (Final Value – Initial Value), is simply the difference between the final value and the initial value. This is called the absolute increase. For example, if the price of a product goes from $100 to $120, the absolute increase is $20.

The second part of the formula, ÷ Initial Value, is to divide the absolute increase by the initial value. This gives the proportion of the increase relative to the initial value. In our example, we divide the absolute increase (20 euros) by the initial value (100 euros), which gives 0,2.

Finally, the last part of the formula, x 100, is to convert this proportion into a percentage. In our example, we multiply 0,2 by 100 to get a percentage increase of 20%.

Using this formula, you can calculate a percentage increase for any pair of initial and final values. It is a powerful tool that can help you understand how values ​​change over time.

Steps to Calculate a Percentage Increase

Now that we have defined what a percentage increase is, let's move on to the steps to calculate a percentage increase. The process is quite simple and can be accomplished in three main steps.

The first step is to determine the absolute increase. This is the difference between the final value and the initial value. For example, if the price of a product increases from 100 euros to 120 euros, the absolute increase is 20 euros (120 euros – 100 euros).

The second step is to divide the absolute increase by the initial value. This gives the proportion of the increase relative to the initial value. In our example, we divide the absolute increase (20 euros) by the initial value (100 euros), which gives 0,2.

The third and final step is to convert this proportion into a percentage. To do this, we multiply the proportion by 100. In our example, we multiply 0,2 by 100 to get a percentage increase of 20%.

It’s important to note that these steps apply to any percentage increase, whether it’s a price increase, a salary increase, or an increase in the number of users on a website. The key is to always start with the initial value and work from there.

By following these steps, you can accurately calculate a percentage increase. However, it is also important to understand how to interpret the result, which we will cover in the next section.

Examples of calculating percentage increase

To illustrate the process of calculating the percentage increase, let's look at some real-world examples.

Example 1: Suppose you received a salary increase. Your initial salary was 2000 euros per month and your new salary is 2 euros per month. What is the percentage increase in your salary?

1. Calculate the absolute increase: 2 euros – 200 euros = 2 euros
2. Divide the absolute increase by the initial value: 200 euros ÷ 2 euros = 000
3. Convert this proportion into a percentage: 0,1 x 100 = 10%

So your salary increased by 10%.

Example 2: You are a business owner and you notice that the number of customers has increased from 500 to 650 in the last month. What is the percentage increase in the number of customers?

1. Calculate the absolute increase: 650 customers – 500 customers = 150 customers
2. Divide the absolute increase by the initial value: 150 customers ÷ 500 customers = 0,3
3. Convert this proportion into a percentage: 0,3 x 100 = 30%

So the number of customers increased by 30%.

These examples show how the percentage increase calculation can be applied to various situations. Whether you are calculating a salary increase, an increase in the number of clients, or any other increase, the process is the same. Just follow the steps and use the formula correctly.

How to interpret the result of the calculation

Once you have calculated a percentage increase, it is equally important to know how to interpret the result. The percentage increase gives an indication of the magnitude of the increase compared to the initial value.

For example, if you calculate a salary increase and you get a result of 10%, this means that your salary has increased by 10% compared to your initial salary. In other words, for every 100 euros of your initial salary, you received a raise of 10 euros.

Similarly, if you are a business owner and you calculate a 20% increase in customers, that means that for every 100 customers you initially had, you gained 20 additional customers.

It is important to note that the percentage increase is a relative measure, not an absolute one. A 50% increase means that the final value is 50% greater than the initial value, not that it is 50% of the initial value. For example, if the price of a product increases from 100 euros to 150 euros, the percentage increase is 50%, not 150%.

Finally, it is also important to understand that the percentage increase does not provide information about the length of time over which the increase occurred. A 20% increase could occur over a period of one month, one year, or ten years. To get information about the speed or rate of increase, you will need to perform additional calculations, such as calculating the compound annual growth rate.

Common Mistakes When Calculating Percentage Increase

When calculating percentage increase, it is important to watch out for some common mistakes. By being aware of these mistakes and knowing how to avoid them, you can ensure that you get accurate results.

The first common mistake is to confuse absolute increase with percentage increase. As we mentioned earlier, absolute increase is simply the difference between the final value and the initial value, while percentage increase is that difference expressed as a percentage of the initial value. Make sure you don't confuse these two concepts.

Another common mistake is to use the final value instead of the initial value in the calculation formula. Remember that the percentage increase is calculated relative to the initial value, not the final value. For example, if the price of a product increases from 100 euros to 120 euros, you must divide the absolute increase (20 euros) by the initial value (100 euros), not by the final value (120 euros).

Finally, another common mistake is not converting the proportion to a percentage at the end of the calculation. After dividing the absolute increase by the initial value, you get a proportion, not a percentage. To convert this proportion to a percentage, you must multiply it by 100.

By avoiding these common mistakes, you can ensure that your percentage increase calculations are accurate and meaningful. Remember, practice is key to mastering this calculation, so feel free to practice with different examples until you feel comfortable.

Use of Percentage Increase in Daily Life

Calculating percentage increases is a useful skill in many aspects of daily life. Here are some examples of situations where you might need to calculate a percentage increase.

First, calculating the percentage increase can help you manage your personal budget. For example, if you are tracking your spending and notice that your grocery spending has increased from $50 to $75, you can calculate the percentage increase to understand the magnitude of this increase. In this case, the percentage increase is 50%, which might prompt you to review your shopping habits to reduce your spending.

Second, calculating the percentage increase can help you evaluate price increases. For example, if your gym membership price goes from $30 per month to $33 per month, the percentage increase is 10%. This information can help you decide if the price increase is reasonable and whether you want to continue your membership.

Third, calculating the percentage increase can help you understand how your financial situation is changing. For example, if you invest money and the value of your investment increases from $1000 to $1200, the percentage increase is 20%. This information can help you evaluate the performance of your investment and make informed financial decisions.

These examples show how the percentage increase calculation can be applied to various aspects of daily life. By mastering this calculation, you can improve your financial management and make more informed decisions.

Use of percentage increase in the professional environment

In the professional environment, calculating the percentage increase is also a valuable tool. It can be used in various contexts, ranging from performance evaluation to market trend analysis. Here are some examples.

First, if you are a manager, you can use the percentage increase calculation to evaluate your team's performance. For example, if the number of projects completed by your team increases from 10 to 15 in a month, the percentage increase is 50%. This information can help you understand the effectiveness of your team and identify areas that need improvement.

Second, if you work in sales or marketing, you can use the percentage increase calculation to analyze market trends. For example, if a product's sales increase from 1 units to 000 units in one month, the percentage increase is 1%. This information can help you understand the market demand for that product and plan your sales and marketing strategies accordingly.

Third, if you work in finance, you can use the percentage increase calculation to evaluate investment performance. For example, if the value of an investment increases from $10 to $000 in one year, the percentage increase is 11%. This information can help you evaluate the profitability of the investment and make informed financial decisions.

These examples show how the percentage increase calculation can be used in a variety of business contexts. By mastering this calculation, you can improve your ability to evaluate performance, analyze market trends, and make informed decisions.

Online tools to calculate a percentage increase

If you prefer to avoid manual calculations, there are several free online tools that can help you calculate a percentage increase. These tools are easy to use and can provide you with accurate results in seconds. Here are some examples.

1. Online Calculators: There are many free online calculators that can calculate a percentage increase. You simply enter the starting value and the ending value, and the calculator will do the rest. Some of these tools also offer detailed explanations of the calculation, which can be helpful if you are trying to understand the process.
   
   
2. Spreadsheets: If you need to calculate percentage increases for a large number of values, a spreadsheet can be a valuable tool. You can use software like Microsoft Excel or Google Sheets to create a formula that calculates the percentage increase. Once you create the formula, you can apply it to all the values ​​in your spreadsheet.
   
   
3. Mobile Apps: If you need to calculate a percentage increase on the go, there are several mobile apps that can help you. These apps work similarly to online calculators, but they are designed to be used on a smartphone or tablet.

These tools can save you time and help you avoid calculation errors. However, it is always helpful to understand how the calculation is performed, so that you can interpret the results correctly.

FAQ: Frequently Asked Questions About Calculating Percentage Increase

It’s completely normal to have questions about how the percentage increase is calculated. Here are some of the most frequently asked questions on this topic, along with their answers.

1. Question: What does a percentage increase of 100% mean?
   • Answer: A percentage increase of 100% means that the final value is twice the initial value. For example, if the price of a product increases from 50 euros to 100 euros, the percentage increase is 100%.
     
     
2. Question: How to calculate a percentage increase if the initial value is zero?
   • Answer: If the initial value is zero, the percentage increase is usually considered infinite, because any increase from zero is an infinite percentage increase. In practice, however, it is often more useful to simply state the absolute increase.
     
     
3. Question: Is percentage increase the same as growth rate?
   • Answer: Percentage increase and growth rate are similar concepts, but they are not exactly the same. Percentage increase measures the magnitude of the increase from the initial value, while growth rate measures the speed of the increase over a specific period of time.
     
     
4. Question: How to calculate the percentage increase if the final value is less than the initial value?
   • Answer: If the final value is less than the initial value, the percentage increase will be negative. This indicates a decrease rather than an increase. For example, if the price of a product goes from 100 euros to 80 euros, the percentage increase is -20%.

These answers should help you better understand the percentage increase calculation. Remember that practice is key to mastering this calculation, so feel free to practice with different examples until you feel comfortable.

Conclusion

In conclusion, knowing how to calculate a percentage increase is a valuable skill that can be used in many aspects of daily and professional life. Whether it's evaluating a salary increase, analyzing market trends, or managing your personal budget, the percentage increase is a powerful tool for understanding how values ​​change over time.

The calculation process is quite simple and is based on a basic mathematical formula. However, it is important to be careful of common mistakes, such as confusing absolute increase with percentage increase, using the final value instead of the initial value in the formula, and forgetting to convert the proportion to a percentage at the end of the calculation.

It is also important to know how to interpret the result of the calculation. A percentage increase of 20% means that the final value is 20% larger than the initial value, not that it is 20% of the initial value. Furthermore, the percentage increase does not give information about the duration over which the increase occurred.

Finally, if you prefer to avoid manual calculations, there are several free online tools that can help you calculate a percentage increase. These tools are easy to use and can provide you with accurate results in seconds.

We hope this guide has helped you understand how to calculate a percentage increase. Remember, practice is key to mastering this calculation, so feel free to practice with different examples until you feel comfortable. Good luck!

9 Corrected exercises to calculate a percentage increase

Burger House App

States :

In the city of Pau, the franchisor of a famous burger restaurant chain "Burger House" is considering increasing the prices of its menus. Faced with strong demand and an increase in production costs, it decides to review its sales prices. Before making any decision, it wants to assess the impact that each price increase would have on its various margins (unit margin, margin on variable costs, margin on fixed costs).

To do this, it has the following information:
– Initial sale price of the standard menu (initial PV) = €12,00
– Unit purchase price of the standard menu (PA) = €5,00
– Quantity currently sold = 10 units
– Annual fixed costs = €50
– Unit variable costs = €2,50

Work to do :

1) Calculate the unit margin and overall margin before the price increase.
2) If the franchisor decides to increase the price of the standard menu by €1, calculate the new unit margin and the new overall margin.
3) What is the percentage increase in the selling price?
4) Calculate the percentage increase in unit margin.
5) Calculate the percentage increase in the overall margin.

Proposed correction:

1) The unit margin is calculated as the difference between the selling price and the purchase price. Here, Unit Margin = Initial PV – PA = €12,00 – €5,00 = €7,00

The overall margin is calculated as the product of the unit margin and the quantity sold. Here, Overall Margin = Unit Margin x Quantity Sold = €7,00 x 10 = €000

2) With the increase of €1, the new selling price will be €13,00. The new unit margin will therefore be €13,00 – €5,00 = €8,00.

The new overall margin will be €8,00 x €10 = €000

3) The percentage increase in the selling price is given by the formula: ((New PV – Old PV) ? Old PV) x 100.
So, ((€13,00 – €12,00) / €12,00) x 100 = 8,33%

4) The percentage increase in unit margin is given by the formula: ((New unit margin – Old unit margin) ? Old unit margin) x 100.
So, ((€8,00 – €7,00) / €7,00) x 100 = 14,29%

5) The percentage increase in the overall margin is given by the formula: ((New overall margin – Old overall margin) ? Old overall margin) x 100.
So, ((€80 – €000) / €70) x 000 = 70%

Summary of Formulas Used:

– Unit margin = Selling price – Purchase price
– Overall margin = Unit margin x Quantity sold
– Percentage increase = ((New value – Old value) ? Old value) x 100.

Bursting Fruits Application

States :

The company "Fruits Éclatants", which specializes in the sale of fresh fruit, is considering increasing the price of its apples. Their current price is €2,00 per kilogram.

In the last few days, the company has received information about the increase in the production and transportation costs of apples from its suppliers. Therefore, they have decided to adjust the price of apples.

Work to do :

1. If “Fruits Éclatants” decides to increase the price of apples by 10%, what will the new price be?
2. How much is the increase in euros?
3. If the company decides to reduce the increased price by 5%, then what will the new price be?
4. How much has the price decreased in euros since the previous 10% increase?
5. What is the percentage discount compared to the 10% increased price?

Proposed correction:

1. To calculate the new price after a 10% increase, we use the formula: new price = current price + (current price x increase rate)
That is: new price = €2,00 + (€2,00 x 10%) = €2,00 + €0,20 = €2,20

2. The amount of the increase in euros is therefore: €2,20 – €2,00 = €0,20

3. To reduce the increased price by 5%, we use the formula: new price = increased price – (increased price x reduction rate)
That is: new price = €2,20 – (€2,20 x 5%) = €2,20 – €0,11 = €2,09

4. The price has decreased by: €2,20 – €2,09 = €0,11 since the previous 10% increase.

5. The percentage reduction compared to the price increased by 10% is: (€0,11 ÷ €2,20) x 100 = 5%

Summary of Formulas Used:

– Increase: new price = current price + (current price x increase rate)
– Recover the increase in euros: Increase in euros = price after increase – price before increase
– Discount: new price = current price – (current price x discount rate)
– Recover the reduction in euros: Reduction in euros = price before reduction – price after reduction
– Conversion of the reduction into a percentage: (reduction in euros ÷ price before reduction) x 100

Paris Shoes App

States :

Mr. Durand is the manager of a small shoe sales company called "Paris Chaussures". He has just implemented a price increase on several items in his store to respond to the increase in production costs and the market. Mr. Durand needs help calculating the percentage of this increase.

An example of affected items would be sports shoes that originally cost €50 and are now sold for €60.

Work to do :

1. How much is the increase in €?
2. How to calculate the percentage increase from the initial price?
3. What is the percentage of the increase?
4. How to calculate the new price after increase from the initial price and the percentage increase?
5. Taking the example of sports shoes, what would the new price be if Mr. Durand decided to apply a 20% increase?

Proposed correction:

1. The increase amount is calculated by subtracting the original price from the new price. So, here the increase is €60 – €50 = €10.

2. The percentage increase is calculated by dividing the increase amount by the original price and multiplying the result by 100. The formula is therefore: (increase ? Original price) x 100 = % increase.

3. Using this formula, the percentage increase on sports shoes is therefore: (€10 ? €50) x 100 = 20%.

4. The new price after increase is calculated by adding the percentage of the increase to the initial price. The formula is therefore: Initial price + (Initial price x % increase ? 100) = New price.

5. If Mr. Durand decided to apply a 20% increase, the new price of sports shoes would therefore be: €50 + (€50 x 20 ? 100) = €60.

Summary of Formulas Used:

– Amount of increase: New price – Initial price.
– Percentage of increase: (Increase ? Initial price) x 100.
– New price after increase: Initial price + (Initial price x % increase ? 100).

TechnoStore Application

States :

The company "TechnoStore", which specializes in the sale of electronic products, has seen a significant increase in its sales over the past year. It wants to calculate the percentage of this increase for each of its flagship products: a laptop, a smartphone and a tablet.

– Initially, TechnoStore sold 200 computers at €750 each. Towards the end of the year, they managed to sell 250 of these same computers.
– For smartphones, they sold 300 to 600 € each at the beginning. Towards the end of the year, they sold 360 smartphones.
– At the beginning of the year, 180 tablets were sold at €400 each. Towards the end of the year, they managed to sell 220 tablets.

Work to do :

1. What is the percentage increase in computer sales?
2. What is the percentage increase in smartphone sales?
3. What is the percentage increase in tablet sales?
4. On average, by what percentage did the sales increase?
5. Which of the three product categories shows the largest percentage increase?

Proposed correction:

1. To calculate the percentage increase in computer sales, we apply the formula: ((New Quantity – Old Quantity) / Old Quantity) x 100. Here, this gives ((250 – 200) ÷ 200) x 100 = 25% increase

2. To calculate the percentage increase in smartphone sales, we apply the formula: ((New Quantity – Old Quantity) / Old Quantity) x 100. Here, this gives ((360 – 300) ÷ 300) x 100 = 20% increase

3. To calculate the percentage increase in tablet sales, we apply the formula: ((New Quantity – Old Quantity) / Old Quantity) x 100. Here, this gives ((220 – 180) ÷ 180) x 100 = 22,22% increase

4. To calculate the average increase, we average the three percentages, i.e. (25 + 20 + 22,22) / 3 = 22,41% average increase

5. Computers show the largest percentage increase of 25%.

Summary of Formulas Used:

Percentage increase = ((New Quantity – Old Quantity) ÷ Old Quantity) x 100

Average Percentage Increase = (Percentage Increase 1 + Percentage Increase 2 + Percentage Increase 3) ÷ Number of Categories

The Golden Sun Application

States :

The company "Le Soleil Doré", which specializes in the sale of bakery products, wants to assess the impact of an increase on its prices. They increased the price of their croissant from €0,90 to €1,10 and that of their pain au chocolat from €1,10 to €1,40. Production costs, however, have not increased.

Work to do :

1. What is the percentage increase in the price of the croissant?
2. What is the percentage increase in the price of pain au chocolat?
3. What is the effect of these increases on the unit margin of each product?
4. What is the new price index for the croissant and the pain au chocolat, if the initial index was 100 for both?
5. If the company sold 1000 croissants and 800 pains au chocolat per day, what would be the impact of these increases on its daily turnover?

Proposed correction:

1. Percentage increase in croissant price = ((Final price – Initial price) / Initial price) x 100
= ((€1,10 – €0,90) / €0,90) x 100 = 22,22%
2. Percentage increase in the price of pain au chocolat = ((Final price – Initial price) / Initial price) x 100
= ((€1,40 – €1,10) / €1,10) x 100 = 27,27%
3. Increasing the selling price without increasing the cost of production results in an increase in the unit margin. The unit margin is now the difference between the new selling price and the initial cost of production.
4. Price index = (Final price / Initial price) x 100
For the croissant: (€1,10 / €0,90) x 100 = 122,22
For the pain au chocolat: (€1,40 / €1,10) x 100 = 127,27
5. Impact on turnover:
For the croissant: (€1,10 – €0,90) x 1000 = €200 extra per day.
For the pain au chocolat: (€1,40 – €1,10) x 800 = €240 extra per day.

Summary of Formulas Used:

– Percentage increase = ((Final price – Initial price) / Initial price) x 100
– Price index = (Final price / Initial price) x 100
– Impact on turnover: (Final price – Initial price) x quantity sold

ABC Fashion App

States :

ABC Fashion Company specializes in selling fashion clothing. At the beginning of the year, the manager decided to increase the price of some items. You are the manager's assistant and you are asked to determine the percentage increase of the different products. Here is some information:

1) The price of a sweater has gone from €30 to €35.
2) The price of a pair of trousers has increased from €45 to €50.
3) The price of a dress has gone from €55 to €65.
4) The price of a coat has increased from €120 to €130.
5) The price of a shirt has increased from €15 to €18.

Work to do :

1) What is the percentage increase in the price of the sweater?
2) What is the percentage increase in the price of the pants?
3) What is the percentage increase in the price of the dress?
4) What is the percentage increase in the price of the coat?
5) What is the percentage increase in the price of the shirt?

Proposed correction:

1) The increase in the sweater is €5. To determine the percentage increase, we use the formula: [(Pf – Pi) / Pi] x 100, where Pf is the final price and Pi is the initial price. Therefore, (5 ÷ 30) x 100 = 16,67%. The price of the sweater has therefore increased by 16,67%.

2) The increase in the price of the pants is €5. Using the same formula, (5 ÷ 45) x 100 = 11,11%. So the price of the pants has increased by 11,11%.

3) The increase in the dress is €10. Therefore, (10 ÷ 55) x 100 = 18,18%. Therefore, the price of the dress has increased by 18,18%.

4) The increase in the price of the coat is €10. Therefore, (10 ÷ 120) x 100 = 8,33%. The price of the coat has therefore increased by 8,33%.

5) The increase in the shirt is €3. Therefore, (3 ÷ 15) x 100 = 20%. The price of the shirt has therefore increased by 20%.

Summary of Formulas Used:

– Percentage increase formula: [(Final price – Initial price) / Initial price] x 100. It is used to calculate the percentage increase of a product.

SOFGYM application

States :

SOFGYM, a company specializing in the sports and wellness industry, has decided to review its prices following an internal restructuring and an increase in production costs.

1. The annual membership fee is currently €250. SOFGYM plans to increase this price by 10%. What will the new price be?

2. The price of individual sessions increases from €20 to €25. What is the percentage of the increase?

3. A nutrition pack that used to cost €50 will now cost €55. What is the rate of increase?

4. SOFGYM has revised the prices of its sportswear. A set that used to cost €75 now costs €86. What is the percentage increase?

5. The company is considering increasing the price of its group fitness classes by 15%. If the current price is €10, what will the new price be?

Work to do :

1. Calculate the new annual membership price after the increase.
2. Calculate the percentage increase in the price of individual sessions.
3. Calculate the rate of increase of the nutrition pack.
4. Calculate the percentage increase in the price of sportswear.
5. Calculate the new price of group fitness classes after the increase.

Proposed correction:

1. The new annual membership price is: €250 + (€250 * 10 / 100) = €250 + €25 = €275.
2. The percentage increase for individual sessions is: ((€25 – €20) ÷ €20) * 100 = 25%.
3. The increase rate of the nutrition pack is: ((€55 – €50) ÷ €50) * 100 = 10%.
4. The percentage increase in the price of sportswear is: ((€86 – €75) ÷ €75) * 100 = 14,67% (rounded to the nearest hundredth).
5. The new price for group fitness classes will be: €10 + (€10 * 15% ÷ 100) = €10 + €1,5 = €11,5.

Summary of Formulas Used:

– New price after increase: Current price + (Current price * Increase rate ÷ 100)
– Percentage increase: ((New price – Old price) ÷ Old price) * 100

Delicious Breads App

States :

Pierre is the owner of the company "Delicious Breads", a famous bakery in town. He recently made an increase on some of his products.

1. Peter increased the price of a baguette from €1,00 to €1,20.
2. The price of the brioche, which was originally €1,50, has been increased to €1,80.
3. The chocolate éclair, previously sold for €2,00, is now €2,40.
4. Raisin bread, which cost €1,10, has increased to €1,40.
5. Finally, the croissant, previously at €0,90, is now sold at €1,10.

Work to do :

1. What is the percentage increase in the price of baguette bread?
2. What is the percentage increase in the price of brioche?
3. What is the percentage increase in the price of chocolate éclairs?
4. What is the percentage increase in the price of raisin bread?
5. What is the percentage increase in the price of the croissant?

Proposed correction:

1. The percentage increase in the price of baguette bread is calculated as follows: ((€1,20 – €1,00) ÷ €1,00) x 100 = 20%

2. The percentage increase in the price of brioche is calculated as follows: ((€1,80 – €1,50) ÷ €1,50) x 100 = 20%

3. For the chocolate éclair, the percentage increase is: ((€2,40 – €2,00) ÷ €2,00) x 100 = 20%

4. The percentage increase in the price of raisin bread is: ((€1,40 – €1,10) ÷ €1,10) x 100 = 27,27% (rounded to the second digit after the decimal point to obtain an accurate percentage)

5. For the croissant, the percentage increase is calculated as follows: ((€1,10 – €0,90) ÷ €0,90) x 100 = 22,22% (rounded to the second digit after the decimal point to obtain an accurate percentage)

Summary of Formulas Used:

– Percentage increase = ((New amount – Old amount) ÷ Old amount) x 100
This formula is used to calculate the percentage of an increase. It helps determine how much a certain amount has been increased in percentage terms.
Note: Results for questions 4 and 5 are rounded to the second decimal place for accuracy.

Summer Fruits Application

States :

Let's study the company "Summer Fruits", a start-up that produces and sells a variety of fruit juices. In the first half of 2021, the selling price (excluding VAT) of a liter of juice was €10. The company recently increased its prices to take into account inflation and increases in raw material costs. The new prices are now €12 per liter (excluding VAT).

Work to do :

1. Calculate the increase in euros.
2. Calculate the percentage increase in the original price.
3. If the company sold 1000 liters of juice in the first half of the year at the old price, what would be the additional revenue generated with the new price, assuming that the sales volume remains the same?
4. If the current VAT is 20%, calculate the new sales price including VAT.
5. Suppose this year's inflation rate is revised to 10%. Will Summer Fruits have to readjust its prices? If so, what will the new price be?

Proposed correction:

1. The increase in euros is the new selling price (€12) minus the old selling price (€10), i.e. €12 – €10 = €2.

2. The percentage increase is known by applying the formula increase ÷ initial price x 100. This therefore gives (€2 ÷ €10) x 100 = 20%.

3. If the company had sold 1000 liters of juice at the new price, the additional revenue would be: (New selling price – Old selling price) x quantity sold = (€12 – €10) x 1000 = €2000.

4. The new sales price including VAT can be calculated by adding VAT to the price excluding VAT. Therefore, the new price including VAT = price excluding VAT (new) + (price excluding VAT (new) x VAT/100). This gives €12 + (€12 x 20 / 100) = €12 + €2,4 = €14,4.

5. If inflation is revised to 10%, the new increase required would therefore be €10 x 10% = €1. So the new selling price would be €10 + €1 = €11. But since they have already increased the price to €12, they do not need to readjust their prices.

Summary of Formulas Used:

1. Increase in euros = New selling price – Old selling price
2. Percentage increase = (Increase in euros ÷ Old selling price) x 100
3. Additional revenue = (New selling price – Old selling price) x Quantity sold
4. Sales price including VAT = price excluding VAT (new) + (price excluding VAT (new) x VAT/100)
5. New price in case of inflation = Old selling price + (Old selling price x Inflation rate / 100)