How to Find the Percentage Between Two Numbers

Welcome to this article on exercises on business calculations and more specifically on how to find the percentage between two numbers. Here you will find questions and answers related to the subject. But also no less than 7 detailed corrected management exercises on business calculations for Operational Management.

By the end of this article, you will know how to find the percentage between two numbers in business calculations without any worries. If you wish, do not hesitate to go directly to the 7 corrected exercises in order to practice.

What is a percentage and how is it calculated?

A percentage is a numerical expression that illustrates a proportion or ratio in terms of 100. It is a multiplier that converts fractions into a more understandable form. Percentage is a whole or decimal value that represents a fraction of a hundred. In mathematics, percentage is a commonly used measure for comparison and statistical analysis. To calculate it, a simple formula is used: (value / base) * 100. This equation can be solved using a calculator or by hand. For example, if you want to express 25 out of 100 as a percentage, you divide 25 by 100 to get 0,25, then multiply by 100 to get 25%. This is a common practice in numerical analysis and data interpretation.

What is the formula to find the percentage between two numbers?

The formula for finding the percentage between two numbers is simple and straightforward. It involves dividing the first number (the value) by the second number (the base), then multiplying the result by 100 to get the percentage. This method is a practical application of mathematical theory. For example, to find the percentage of 50 to 200, you divide 50 by 200 to get 0,25, then multiply by 100 to get 25%. This is a quick and accurate approach to estimating proportions.

How to interpret the result obtained by calculating the percentage between two numbers

The interpretation of the result obtained by calculating the percentage between two numbers depends on the context. In general, the percentage indicates the proportion of the first number (the value) in relation to the second (the base). For example, a percentage of 20% means that the value represents 20% of the base. This interpretation can be qualitative or quantitative, relative or absolute, depending on the context. From a critical perspective, it is important to understand the meaning of the percentage and its implication in data analysis.

In what practical cases would it be useful to calculate the percentage between two numbers?

Calculating the percentage between two numbers is useful in many practical cases. In finance, it can be used to determine the proportion of an investment in a portfolio or the share of a product in a company's total sales. In business, it can help calculate discounts or price increases. In education, it can be used to evaluate student performance or to measure the progress of a curriculum. In project management, it can help estimate the progress of a project or the effectiveness of a strategy. In economics, it can be used to analyze the distribution of income or the consumption of resources.

Are there any tools or apps that can help find the percentage between two numbers?

Yes, there are many tools and applications that can help in finding the percentage between two numbers. For example, digital calculators, programming software, data analysis algorithms, and mobile applications available on the App Store or Google Play. These tools offer advanced features, intuitive user interface, high accuracy, and connectivity with other applications or databases. They are regularly updated to improve their performance and efficiency.

How can calculating the percentage between two numbers be applied in the financial field?

In the financial field, calculating the percentage between two numbers is often used to assess the profitability of an investment, the risk of a portfolio, the yield of a stock or bond, the interest rate of a loan, the performance of a market, the liquidity of an account, etc. For example, to calculate the return on an investment, we divide the profit by the invested capital and multiply the result by 100. This analysis allows us to make informed decisions and manage financial transactions efficiently.

How can calculating the percentage between two numbers be applied in the field of education?

In education, calculating the percentage between two numbers is often used to assess student performance, measure curriculum progress, compare exam results, determine a student's grade, etc. For example, to calculate a student's score, divide the number of points obtained by the total number of possible points and multiply the result by 100. This method helps assess the effectiveness of teaching and learning, and improve teaching methods.

What are the common mistakes to avoid when calculating the percentage between two numbers?

When calculating the percentage between two numbers, it is important to avoid some common mistakes, such as reversing the formula, forgetting to multiply by 100, misinterpreting the result, using incorrect data, applying inappropriate methods, etc. It is also important to check the accuracy of the calculation, check the variables and parameters, and correct any mistakes. A good practice is to make a quick estimate before performing the calculation to check the consistency of the result.

How does calculating the percentage between two numbers differ from calculating the percentage of a single number?

Calculating the percentage between two numbers involves dividing the first number by the second and multiplying the result by 100. In contrast, calculating the percentage of a single number involves multiplying it by the given percentage. For example, to find 20% of a number, you multiply it by 0,20. So, while both methods involve percentages, they are used in different contexts and require different adjustments to get an accurate result.

Are there any concrete examples illustrating the calculation of the percentage between two numbers in daily life?

Yes, there are many real-world examples of calculating the percentage between two numbers in everyday life. For example, to calculate the proportion of your income that goes to savings, you divide the amount saved by your total income and multiply the result by 100. To determine the discount you get on a sale, you divide the price difference by the original price and multiply the result by 100. These examples show how calculating the percentage can be used to manage your personal finances, make purchases, sell products, evaluate offers, and more.

7 Corrected Applications on How to Find the Percentage Between Two Numbers

Summary of the formulas applied:

States	Variables / Formulas	Description
Tech Innov
1	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Calculation of the margin rate
2	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	Calculation of the mark rate
3	Percentage increase = (?Profit ÷ Initial Profit) x 100	Percentage increase in profit
4	Percentage of loss = (Loss ÷ Initial investment) x 100	Percentage of loss
5	New price after discount = Initial price x (1 – Discount rate)	Calculation of the new price after discount
zephyr
1	Overall margin = Unit margin x quantity sold	Calculation of the overall margin
2	Margin ratio = (Overall Margin B ÷ Overall Margin A) x 100	Calculation of the margin ratio
3	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Calculation of the margin rate
4	Comparison of unit margins = ((Unit Margin A ÷ Unit Margin B) x 100)	Comparison of unit margins
Sparkling Treasures
1	Percentage Change = (Final Amount – Initial Amount) ÷ Initial Amount x 100	Percentage change in turnover
2	Absolute drop in turnover = Initial amount – Final amount	Calculation of the absolute drop in turnover
3	Revenue forecast = Initial amount x (1 + Percentage increase ÷ 100)	CA forecasts after increase
4	Percentage of an amount = Partial amount ÷ Total amount x 100	Percentage of one value relative to another
5	Growth Percentage = (Final Amount – Initial Amount) ÷ Initial Amount x 100	Percentage of turnover growth
Luxury Food
1,2,3	Percentage increase or decrease = (Final value – Initial value)/Initial value × 100	Percentage variation
4	Percentage that one value represents relative to another = (Value / Total) x 100	Percentage of a value in the total
Gourmet Delight
1,2	Percentage = (part ÷ total) x 100	Percentage of a part in the total
5	Percentage increase = ((new value – old value) ÷ old value) x 100	Percentage increase
Unicorn Widgets
1,2,3	Percentage increase = ((Final value – Initial value) ÷ Initial value) x 100	Percentage increase or decrease
TechStep
1,2,4,5	Percentage of total = (Part ÷ Total) x 100	Percentage of a part in the total
5	Percentage of impact on total = (Percentage of one part x Percentage of change of that part)	Percentage of impact on the total due to the change of one part

Note:

• PV HT: Sale Price Excluding Tax
• PA HT: Purchase Price Excluding Tax

Tech Innov Application

The company Tech Innov, which specializes in the sale of computer equipment, carries out a financial analysis of its sales.

1. The company sold 2 laptops at €500 each excluding VAT during the year. The unit purchase excluding VAT of these laptops is €800. What is the company's margin rate on this sale?

2. Furthermore, the company sold 1 tablets at €000 each excluding VAT. The unit purchase cost of these tablets is €400 excluding VAT. What is the markup rate for this sale?

3. During the year, the company's net profit increased by €12 to €000. What is the percentage increase in this profit?

4. The company made an investment that generated a loss of €4, compared to an initial investment of €000. What is the percentage of the loss?

5. To clear its inventory, the company has given a 20% discount on laptops that originally cost €1 excluding VAT. What is the new price excluding VAT after the discount?

Work to do :

You need to calculate the margin rates, markup rates, increase or loss percentages and the new price excluding VAT after the discount.

Proposed correction:

1. The margin rate is given by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.

In this case, the profit of each computer is €800 – €500 = €300.

So the profit ratio on the purchase cost is 300€ ÷ 500€ = 0,6. The margin rate is therefore 0,6 x 100 = 60%.

2. The markup rate is given by the formula: ((PV HT – PA HT) ÷ PV HT) x 100.

Here, the profit per tablet is €400 – €250 = €150.

The profit ratio on the sale price is therefore 150€ ÷ 400€ = 0,375. The markup rate is therefore 0,375 x 100 = 37,5%.

3. The percentage of profit increase is given by the formula: (?Profit ÷ Initial Profit) x 100.

In this case, ?Profit is €12, and the initial profit is therefore €000 – €62 = €000. The percentage increase is therefore (€12 ÷ €000) x 50 = 000%.

4. The percentage of loss is given by the formula: (Loss ÷ Initial investment) x 100.

Here the loss is €4 and the initial investment is €000. The percentage of the loss is therefore (€20 ÷ €000) x 4 = 000%.

5. The new price excluding VAT after the discount is given by the formula: Initial price excluding VAT x (1 – Discount rate). In this case, the discount rate is 20%, so the new price is €1 x (000 – 1) = €0,2.

Summary of Formulas Used:

– Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100
– Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100
– Percentage increase = (?Value ÷ Initial value) x 100
– Percentage of loss = (Loss ÷ Initial investment) x 100
– New price after discount = Initial price x (1 – Discount rate)

Zephyr App

Zephyr Company, which specializes in the sale of computer equipment, wishes to better understand its sales performance on products A and B.

Product A:
– Quantity sold in the month: 1000 units.
– Purchase price excluding VAT per unit: €10,00.
– Selling price excluding VAT per unit: €15,00.

Product B:
– Quantity sold in the month: 800 units.
– Purchase price excluding VAT per unit: €12,00.
– Selling price excluding VAT per unit: €20,00.

The VAT rate is 20% for both products.

Work to do :

1. Calculate the overall margin made on product A.
2. Calculate the overall margin made on product B.
3. Give as a percentage the ratio of the overall margin of product B to that of product A.
4. Calculate the margin rate for each product.
5. Estimate the percentage of the unit margin achieved on product A compared to that of product B.

Proposed correction:

1. The overall margin on product A is calculated as follows: Unit margin x quantity sold = (PV HT – PA HT) x quantity sold = (€15,00 – €10,00) x 1000 = €5.

2. The overall margin on product B is calculated as follows: Unit margin * quantity sold = (PV HT – PA HT) * quantity sold = (€20,00 – €12,00) x 800 = €6.

3. The ratio of the overall margin of product B to that of product A is: (Overall margin B ÷ Overall margin A) x 100 = (€6 ÷ €400,00) x 5 = 000,00%.

4. The margin rate for each product is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.

– Product margin rate A = ((€15,00 – €10,00) ÷ €10,00) x 100 = 50%.

– Product margin rate B = ((€20,00 – €12,00) ÷ €12,00) x 100 = 66,67%.

5. The percentage of the unit margin achieved on product A compared to that of product B is: ((Unit margin A ÷ Unit margin B) x 100) = ((€5,00 ÷ €8,00) x 100) = 62,5%.

Summary of Formulas Used:

– Overall margin = Unit margin x quantity sold.
– Margin ratio = (Overall margin B ÷ Overall margin A) x 100.
– Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
– Comparison of unit margins = ((Unit Margin A ÷ Unit Margin B) x 100).

Sparkling Treasures App

Mr. Dubois is the owner of a jewelry store called "Trésors Étincelants". During the year 2020, Mr. Dubois had a prosperous year, his company achieved a turnover of €150. However, at the dawn of 000, due to the economic crisis caused by the pandemic, the turnover dropped to €2021. Mr. Dubois wants to assess the impact of this development on his turnover.

Work to do :

1. Calculate the percentage decrease in turnover between 2020 and 2021.
2. Calculate the absolute amount of this drop in turnover.
3. Mr. Dubois expects a 15% increase in turnover for the year 2022. What will be the estimated turnover for this year?
4. If in 2022 the turnover reaches €125, what will this value represent as a percentage compared to 000?
5. What is the percentage growth in turnover for the year 2022 compared to the year 2020, knowing that the turnover for 2022 is €125?

Proposed correction:

1. To calculate the percentage decrease in turnover between 2020 and 2021, we use the formula: (Initial amount – Final amount) ÷ Initial amount x 100. Therefore, (€150 – €000) ÷ €105 x 000 = 150%.

So there was a 30% drop.

2. The absolute drop in turnover is simply the difference between the turnover of 2020 and that of 2021, i.e. €150 – €000 = €105.

The reduction is therefore €45.

3. To forecast the turnover for the year 2022 assuming an increase of 15%, we use the formula: Initial amount x (1 + Percentage increase ÷ 100).

So, €105 x (000 + 1% ÷ 15) = €100. The expected turnover for 120 is therefore €750.

4. To determine the percentage share of the figure of €125 in relation to €000, we use the formula: Partial amount ÷ Total amount x 105.

So, €125 ÷ €000 x 105 = 000%. This turnover therefore represents 100% compared to that of the year 119,05.

5. To calculate the growth percentage between 2020 (€150) and 000 (€2022), we will use the formula: (Final amount – Initial amount) ÷ Initial amount x 125. Therefore, (€000 – €100) ÷ €125 x 000 = -150%.

This means that there has been a 16,67% reduction in turnover between 2020 and 2022.

Summary of Formulas Used:

1. Percentage change: (Final amount – Initial amount) ÷ Initial amount x 100
2. Absolute drop in turnover: Initial amount – Final amount
3. Revenue forecast: Initial amount x (1 + Percentage increase ÷ 100)
4. Percentage of an amount: Partial amount ÷ Total amount x 100
5. Growth Percentage: (Final Amount – Initial Amount) ÷ Initial Amount x 100

LuxuryFood App

The company LuxuryFood specializes in the sale of high-quality food products. It wants to improve its financial management by observing the variations in its figures over different periods. These variations will be expressed as a percentage.

Here are some data:

– Turnover in 2020: €300
– Turnover in 2021: €330
– Payroll in 2020: €120
– Payroll in 2021: €132
– Number of customers in 2020: 1
– Number of customers in 2021: 1

Work to do :

1. What is the percentage increase in turnover from 2020 to 2021?
2. What is the percentage increase in payroll from 2020 to 2021?
3. What is the percentage increase in the number of customers from 2020 to 2021?
4. In 2021, what percentage does payroll represent in relation to turnover?
5. Compared to 2020, what percentage does the 2021 turnover represent?

Proposed correction:

1. To find the percentage increase in revenue from 2020 to 2021, we use the formula: (Ending Value – Initial Value) ÷ Initial Value × 100.

So: ((€330 – €000) ÷ €300) x 000 = 300%. So the turnover increased by 000% from 100 to 10.

2. To calculate the percentage increase in payroll from 2020 to 2021, we use the same formula: ((€132 – €000) ÷ €120) x 000 = 120%. So payroll increased by 000% from 100 to 10.

3. The percentage increase in the number of customers from 2020 to 2021 is: ((1 – 300) ÷ 1) x 200 = 1%. Therefore, the number of customers increased by 200% from 100 to 8,33.

4. In 2021, the percentage that payroll represents in relation to turnover is calculated as follows: (Payroll ÷ Turnover) x 100.

That is: (€132 ÷ €000) x 330 = 000%. The payroll therefore represents 100% of turnover in 40.

5. To find the percentage that 2021 revenue represents compared to 2020 revenue, we use the formula: (2021 Revenue ÷ 2020 Revenue) x 100.

That is: (€330 ÷ €000) x 300 = 000%. Therefore, the 100 turnover represents 110% of that of 2021.

Summary of Formulas Used:

– Percentage increase or decrease: (Final value – Initial value)/Initial value × 100
– Percentage that one value represents in relation to another: (Value / Total) x 100

Gourmet Delight App

Les Etablissements Gourmet Delight, a company specializing in the sale of luxury food products, conducted a survey among its customers in order to better understand their purchasing behaviors. The study included 200 customers. Of these customers, 80 said that they prefer purchasing seafood products, while 120 said that they prefer purchasing baked goods.

Work to do :

Question 1: What percentage of customers prefer to purchase seafood products?
Question 2: What percentage of customers prefer to buy baked goods?
Question 3: According to the survey, how many customers were surveyed in total?
Question 4: What percentage of customers do not have a specific interest in seafood or bakery products?
Question 5: What is the percentage increase in customers who prefer bakery over seafood?

Proposed correction:

Question 1: The percentage of customers who prefer to purchase seafood products is calculated as follows: (Number of customers who prefer seafood products ÷ total number of customers) x 100 = (80 ÷ 200) x 100 = 40%

Question 2: The percentage of customers who prefer to buy bakery products is calculated as follows: (number of customers preferring bakery products ÷ total number of customers) x 100 = (120 ÷ 200) x 100 = 60%

Question 3: According to the survey, 200 customers were interviewed in total.

Question 4: The percentage of customers who do not have a specific interest in seafood or bakery products is calculated by subtracting customers who prefer these products from the total customers. In this case, it is (200 – 80 – 120) x 100 ÷ 200 = 0%.

Question 5: The percentage increase in the number of customers who prefer bakery over seafood is calculated as follows: ((number of customers who prefer bakery – number of customers who prefer seafood products) ÷ number of customers who prefer seafood products) x 100 = ((120 – 80) ÷ 80 ) x 100 = 50%

Summary of Formulas used:

Percentage = (part ÷ total) x 100
Percentage increase = ((new value – old value) ÷ old value) x 100

Unicorn Widgets App

Unicorn Widgets Company is a company that manufactures and sells different kinds of widgets. In the last few months, the company has seen an increase in sales and profits. The CFO wants to understand the evolution of sales and profits and how these two are related to each other. He will analyze the company's financial reports and find the percentage between two specific numbers.

The following data is extracted from the financial report:

1. The turnover for the first quarter is €250 and for the second quarter is €000.
2. The total production cost for the first quarter is €150 and for the second quarter is €000.
3. The net profit for the first quarter is €35 and for the second quarter is €000.

Work to do :

1. What is the percentage increase in sales from the first quarter to the second quarter?
2. What is the percentage increase in production costs from the first quarter to the second quarter?
3. What is the percentage increase in net profit from the first quarter to the second quarter?
4. What do these percentages mean for the financial health of the company?
5. How can the company use this information to make better financial decisions in the future?

Proposed correction:

1. The percentage increase in sales from the first quarter to the second quarter is calculated using the formula: ((Ending Value – Initial Value) ÷ Initial Value) x 100.

In the given context, it will therefore be ((300 – 000) ÷ 250) x 000 = 250%.

2. The percentage increase in production costs is calculated in the same way. It will therefore be ((200 – 000) ÷ 150) x 000 = 150%.

3. The percentage increase in net profit from the first quarter to the second quarter is ((45 – 000) ÷ 35) x 000 = 35%.

4. The calculated percentages show that the sales and profit of Unicorn Widgets Company have increased significantly. However, the cost of production has also increased, which could affect the overall margin rate. Therefore, it is important to keep a close eye on the costs to maintain the profitability of the company.

5. The company can use this information to perform a more in-depth analysis of production costs and find ways to optimize them.

Additionally, the increase in sales indicates a growing demand for their widgets. They may decide to invest more in production or in new technologies to increase their production capacity.

Summary of Formulas Used:

– Percentage increase = ((Final value – Initial value) ÷ Initial value) x 100.

TechStep Application

Consider the case of TechStep, a technology company that began selling two of its best-selling products, Product Alpha and Product Bravo. The company sold 560 units of Product Alpha for a total of €280 and 000 units of Product Bravo for a total of €400.

Work to do :

1. What is the percentage of units sold of Product Alpha compared to the total units sold for both products?
2. What is the percentage of the total sales amount of Product Bravo compared to the total sales amount for both products?
3. Compare the contribution of each product to total sales. Which product has a higher percentage contribution?
4. If the company plans to increase the price of Alpha product by 5%, what will be the percentage impact on total revenue?
5. If the company expects a 10% increase in sales of the Bravo product, what would be the percentage impact on the total number of units sold?

Proposed correction:

1. The percentage of units sold of Product Alpha is calculated as follows: (number of units of Product Alpha ÷ total units sold) x 100 = (560 ÷ (560+400)) x 100 = 58,33%


2. The percentage of the total sales amount of the Bravo Product is calculated as follows: (total sales amount of the Bravo Product ÷ total sales) x 100 = (€220 ÷ (€000 + €220)) x 000 = 280%


3. Although Product Alpha represents a higher percentage of units sold, Product Bravo represents a higher percentage of total revenue due to its higher monetary value.


4. Increasing the price of Product Alpha by 5% will have an impact on total revenue that is calculated as follows: (percentage of Product Alpha revenue x price increase) = 56% x 5% = 2,8%. This implies a 2,8% increase in total revenue.


5. A 10% increase in sales of Product Bravo would have an impact on total units sold calculated as follows: (400 units x 10%) ÷ (560 + 400) x 100 = 4,76% of total units, which means a 4,76% increase in total units sold.

Summary of Formulas Used:

– Percentage of total = (Part ÷ Total) x 100
– Percentage of impact on the total = (Percentage of a part x Percentage of change of this part)