Welcome to this article on exercises on business calculations and more specifically on how to calculate a percentage discount. Here you will find no less than 11 detailed corrected management exercises on business calculations for Operational Management.
By the end of this article, you will know how to calculate a percentage discount in business calculations without any worries.
In this section:
StyleChic App
States :
In the ready-to-wear company StyleChic, the manager has decided to offer discounts on certain items to attract more customers and increase sales volume. You are responsible for calculating the rate of these discounts. Here are some examples of discounts offered by the company StyleChic:
1. For a dress whose original price is €85, a discount of €17 has been applied.
2. A sweater initially sold for €45 was discounted by €9.
3. A pair of €60 trousers has been reduced by €12.
4. A jacket costing €120 has been discounted by €30.
5. Shoes worth €105 were discounted by €21.
Work to do :
1. What is the discount rate applied to the dress?
2. What is the discount rate on the sweater?
3. What is the discount rate given on the pants?
4. What is the discount rate on the jacket?
5. What is the discount rate applied to shoes?
Proposed correction:
The formula to calculate the discount rate is: Discount Rate = (Discount Amount / Price Before Discount) x 100.
1. The discount applied to the dress is: (17€ / 85€) x 100 = 20%
2. The discount granted on the sweater is: (9€ / 45€) x 100 = 20%
3. The discount rate granted on the pants is: (12€ / 60€) x 100 = 20%
4. The discount rate on the jacket is: (€30 / €120) x 100 = 25%
5. The discount rate applied to shoes is: (€21 / €105) x 100 = 20%
Summary of Formulas Used:
– Discount rate = (Discount amount / Price before discount) x 100
Application The Golden Words
States :
The bookstore Les mots d'or offers a variety of books. In order to encourage reading, the manager decides to organize a sale with discounts on certain books.
The following information is available:
1. The book “The Adventures of the Hero” costs €25 without discount. During the sale, its price is reduced to €20.
2. The book “Passage to the Unknown” costs €15 without discount. During the sale, its price is reduced to €13,50.
3. The book “At the Heart of Science” costs €30 without a discount. During the sale, its price is reduced to €27.
4. The book "Mysteries of History" costs €20 without discount. During the sale, its price is reduced to €18.
5. The book “Fantastic Tales” costs €10 without a discount. During the sale, its price is reduced to €9.
Work to do :
1. What is the percentage discount applied to the book “The Adventures of the Hero”?
2. What is the percentage discount applied to the book “Passage to the Unknown”?
3. What is the percentage discount applied to the book “At the Heart of Science”?
4. What is the discount percentage applied to the book “Mysteries of History”?
5. What is the percentage discount applied to the book “Fantastic Tales”?
Proposed correction:
The formula for calculating a percentage discount is:
Discount percentage = ((Original price – Price after discount) / Original price) x 100
1. Discount percentage on the book “The Adventures of the Hero” = ((€25 – €20) / €25) x 100 = 20%.
2. Discount percentage on the book “Passage to the Unknown” = ((€15 – €13,50) / €15) x 100 = 10%.
3. Discount percentage on the book “At the heart of science” = ((€30 – €27) / €30) x 100 = 10%.
4. Discount percentage on the book “Mysteries of History” = ((€20 – €18) / €20) x 100 = 10%.
5. Discount percentage on the book “Fantastic Tales” = ((€10 – €9) / €10) x 100 = 10%.
Summary of Formulas Used:
Discount percentage = ((Original price – Price after discount) / Original price) x 100
Cozy Home App
States :
Sarah is the financial manager of the company Maison Cosy. This store, specialized in the sale of furniture and interior decoration, often offers promotions to its customers.
One day, the manager decides to have a flash sale on some items, including a sofa that originally cost €750. Sarah then has to calculate the discounts for several discount scenarios for this flash sale.
Work to do :
1. Calculate the price of the sofa if a 10% discount is applied.
2. Calculate the price of the sofa if a 25% discount is applied.
3. Calculate the price of the sofa if a 50% discount is applied.
4. Calculate the price of the sofa if a 75% discount is applied.
5. What would be the discount percentage if the sofa is sold at €550?
Proposed correction:
1. Price after 10% discount = Original price – (Original price x 10%)
Price after discount = €750 – (€750 x 10 / 100)
Price after discount = €750 – €75 = €675.
2. Price after 25% discount = Original price – (Original price x 25%)
Price after discount = €750 – (€750 x 25 / 100)
Price after discount = €750 – €187,50 = €562,50.
3. Price after 50% discount = Original price – (Original price x 50%)
Price after discount = €750 – (€750 x 50 / 100)
Price after discount = €750 – €375 = €375.
4. Price after 75% discount = Original price – (Original price x 75%)
Price after discount = €750 – (€750 x 75 / 100)
Price after discount = €750 – €562,50 = €187,50.
5. Discount percentage = ((Original price – Sale price) / Original price) x 100
Discount percentage = ((€750 – €550) / €750) x 100
Discount percentage = (€200 / €750) x 100 = 26,67% (rounded to two decimal places)
Summary of Formulas Used:
1. Calculation of the discount amount: Initial amount x discount rate (%)
2. Calculation of the price after discount: Initial amount – Discount amount
3. Calculation of the discount percentage: ((Initial price – Sale price) / Initial price) x 100.
Fashion Retail Application
States :
Fashion Retail sells a dress to its customers. The initial sale price of the dress is €80. Fashion Retail decides to offer a discount on this product.
Work to do :
1/ If the price is reduced by €15, what is the percentage of the discount?
2/ If the price is reduced by 20%, what is the new price of the dress?
3/ If the price is reduced by 50%, what is the new price of the dress?
4/ If the price is reduced to €40, what is the percentage of the discount?
5/ If the price is reduced by 25%, what is the new price of the dress?
Proposed correction:
1/ The discount percentage is calculated as follows: (Discount amount ÷ Initial price) x 100
That is, (15 ÷ 80) x 100 = 18,75%
So the discount percentage is 18,75%.
2/ To find the new price after a 20% discount, we use the formula: Initial price x (1 – Discount rate)
That is, 80 x (1 – 20/100) = €64
So the new price of the dress after a 20% discount would be €64.
3/ Similarly, for a 50% discount: 80 x (1 – 50/100) = €40
So the new price of the dress after a 50% discount would be €40.
4/ To calculate the discount percentage when the new price is known, we use the formula: ((Initial price – New price) ÷ Initial price) x 100
That is, ((80 – 40) ÷ 80) x 100 = 50%
So the discount percentage when the price is reduced to €40 is 50%.
5/ Finally, for a 25% discount: 80 x (1 – 25 /100) = €60
So the new price of the dress after a 25% discount would be €60.
Summary of Formulas Used:
– Discount percentage: (Discount amount ÷ Initial price) x 100
– New price after discount: Initial price x (1 – Discount rate)
– Discount percentage when the new price is known: ((Initial price – New price) ÷ Initial price) x 100
Hautain DeBordeaux Application
States :
Your friend, Hautain DeBordeaux, is the owner of a wine shop in the countryside. He wants to run a promotion on one of his bottles of Baux Rouges, an excellent wine that he usually sells for €60 per bottle. In order to increase his sales, he plans to offer a €10 discount on each bottle sold for a week. However, he has not taken the time to calculate this discount as a percentage.
Your friend asks you for help in carrying out these calculations, by asking you the following questions:
Work to do :
1. What is the initial amount of the bottle of wine before discount?
2. What is the value of the reduction in euros?
3. Calculate the price of the wine after the discount.
4. What is the percentage of the discount offered by Hautain?
5. If I have 105 bottles in stock, how much will I lose in total if I sell them all with the discount?
Proposed correction:
1. The initial amount of the bottle of wine before reduction is €60.
2. The value of the reduction in euros is 10€.
3. The price of the wine after the discount is calculated by subtracting the discount from the initial price. So €60 – €10 = €50.
4. The percentage of the discount is calculated by dividing the discount in euros by the original price, then multiplying by 100. So (10€ / 60€) x 100 = 16,67%. Hautain therefore offers a discount of approximately 17%.
5. If Hautain has 105 bottles in stock, the total amount of the discount will be 105 x 10€ = 1050€. Hautain will therefore lose 1050€ in total if he sells all the bottles with the discount.
Summary of Formulas Used:
1. Price after reduction = Initial price – Reduction in euros
2. Discount percentage = (Discount in euros / Initial price) x 100
3. Total amount of loss = Number of bottles in stock x Reduction in euros
EuroDiscount App
States :
The company EuroDiscount, specialized in the sale of household appliances, offers its customers various promotional operations, including percentage discounts. This year, the company wants to analyze and evaluate the impact of these discounts on its margins and prices.
- The Aquamax washing machine, which usually sells for €600 excluding VAT, was offered with a 15% discount during a sale period.
- The FrigoPro refrigerator, which usually costs €1000 excluding VAT, has benefited from a 20% discount.
- The MaxMix mixer, sold at €75 excluding VAT, is offered with a 25% discount
Here are the purchase costs excluding tax for the products: Aquamax (€350), FrigoPro (€700), MaxMix (€30).
Work to do :
1. Calculate the discount amount for each product and the new sales price excluding VAT accordingly.
2. Calculate the margin rate before and after the discount for each product.
3. Evaluate the impact of these discounts on the company's overall margin.
4. Which product has the largest drop in margin rate following the discount?
5. Can the company afford to offer such promotions regularly or should it re-evaluate its discount strategy?
Proposed correction:
1.
– For the Aquamax: Discount = 15/100 x 600 = €90. New price excluding VAT = 600 – 90 = €510.
– For the FrigoPro: Discount = 20/100 x 1000 = €200. New price excluding VAT = 1000 – 200 = €800.
– For MaxMix: Discount = 25/100 x 75 = €18.75. New price excluding VAT = 75 – 18.75 = €56.25.
2.
– For the Aquamax:
– Margin rate before discount = ((600 – 350) / 350) x 100 = 71.43%.
– Margin rate after discount = ((510 – 350) / 350) x 100 = 45.71%.
– For the FrigoPro:
– Margin rate before discount = ((1000 – 700) / 700) x 100 = 42.86%.
– Margin rate after discount = ((800 – 700) / 700) x 100 = 14.29%.
– For the MaxMix:
– Margin rate before discount = ((75 – 30) / 30) x 100 = 150%.
– Margin rate after discount = ((56.25 – 30) / 30) x 100 = 87.5%.
3. With the available data, we can calculate the impact on the overall margin by summing the products of the unit margins and the quantities sold for each product:
Total margin before discounts = (600 – 350) + (1000 – 700) + (75 – 30) = €595
Total margin after discounts = (510 – 350) + (800 – 700) + (56.25 – 30) = €286.25
Percentage impact on margin = ((595 – 286.25) / 595) x 100 = 51.9%
4. FrigoPro has the largest drop in margin rate (from 42.86% to 14.29%), a drop of 66.67%.
5. If the company wants to maintain its profitability, it must be careful in its discount policy. A 51.9% drop in overall profit can be problematic in the long run. It must therefore review its discount strategy, taking care not to impact its margin too much.
Summary of Formulas Used:
– Discount in € = % discount / 100 x Initial price excluding VAT
– New Price excluding VAT = Initial Price excluding VAT – Discount in €
– Margin rate = ((Selling price excluding VAT – Purchase cost excluding VAT) / Purchase cost excluding VAT) x 100
– Overall margin before/after discounts = ?(Selling price excluding VAT – purchase cost excluding VAT) for each product before/after discounts
– Impact on margin = ((total margin before discounts – total margin after discounts) / total margin before discounts) x 100
– Margin rate decrease = ((margin rate before discount – margin rate after discount) / margin rate before discount) x 100
Frisboy App
States :
An amazing hair salon, Frisboy, offers special discounts to its customers every month. This month, they are offering a 20% discount on their most popular service: a haircut, which has a regular price of €50.
Work to do :
1. How much would the service cost the customer after the discount?
2. How many euros does the customer save thanks to the discount?
3. If the discount had been 25%, how much would the service cost?
4. How many euros does the customer save if the discount is 25%?
5. If the service was on sale for €35 after the discount, what was the discount percentage?
Proposed correction:
1. To find the cost of the service after the discount, we use the following formula: Base Price – (Base Price x Discount Percentage). So, €50 – (€50 x 20/100) = €50 – €10 = €40. So the service would cost the customer €40 after the discount.
2. The customer saves the amount of the discount, which is €50 x 20/100 = €10. The customer therefore saves €10.
3. If the discount was 25%, the service would cost: €50 – (€50 x 25/100) = €50 – €12,5 = €37,5. So, if the discount was 25%, the service would cost €37,5.
4. With a 25% discount, the customer would save: €50 x 25/100 = €12,5. So, the customer saves €12,5.
5. If the service was on sale for €35 after the discount, the discount percentage would be: ((€50 – €35) / €50) x 100 = 15/50 x 100 = 30%. So the discount was 30%.
Summary of Formulas Used:
– To calculate the cost after the discount: Base price – (Base price x discount percentage)
– To calculate the discount amount: Base price x discount percentage
– To calculate the discount percentage if we know the price after the discount: ((Base price – Price after discount) ÷ Base price) x 100
Fashion Chic App
States :
Fashion Chic fashion boutique offers various trendy clothes to its customers throughout the year. At the end of the season, the boutique organizes a big sale with discounts on several items.
A particular pair of pants that were originally sold for €60 are now being offered at a 15% discount. Later in the sale, the store decides to offer an additional 10% discount on the already reduced price.
Work to do :
1. How much is the discount for the first reduction?
2. What is the new price after the first discount?
3. How much is the discount for the second reduction?
4. What is the new final price after the second discount?
5. What is the total value of the percentage discount on the original price?
Proposed correction:
1. To calculate the discount amount for the first reduction, we use the formula: (Initial price x discount rate) ÷ 100. So, (€60 x 15) ÷ 100 = €9
2. The new price after the first reduction can be calculated by subtracting the discount from the initial price: €60 – €9 = €51
3. To calculate the discount amount for the second reduction, we use the same formula on the new price: (Reduced price x discount rate) ÷ 100. So, (€51 x 10) ÷ 100 = €5,10
4. The new final price after the second discount can be calculated by subtracting the second discount from the reduced price: €51 – €5,10 = €45,90
5. To find the total value of the percentage discount on the original price, we add the two discount rates offered: 15% + 10%.
However, this gives 25% which would be correct if the second discount had been applied to the original price. In reality, the second discount was applied after the first, so the actual discount is slightly less than 25%.
So we need to use this formula to get the total discount as a percentage: 100 x (1 – (Final Price ÷ Initial Price)). So, 100 x (1 – (€45,90 ÷ €60)) = 23,5%
Summary of Formulas Used:
– Discount amount = (Initial price x discount rate) ÷ 100
– New price after reduction = Initial price – Discount amount
– Total percentage discount = 100 x (1 – (Final Price ÷ Initial Price))
Elegance Jewel Application
States :
The company Bijou Élégance, which specializes in jewelry design, has decided to organize an exceptional sale during which it is offering a discount on some of its products.
The owner, Mr. Dubois, sets the selling prices (PV) of the products as follows:
– Gold bracelet: €2000
– Diamond necklace: €5000
– Silver watch: €1500
Mr. Dubois has decided to offer discounts on his products:
– Gold bracelet: €300 discount
– Diamond necklace: €1000 discount
– Silver watch: €200 discount
Work to do :
1. Calculate the percentage discount for the gold bracelet.
2. Calculate the percentage discount for the diamond necklace.
3. Calculate the percentage discount for the silver watch.
4. Which product has the biggest percentage discount?
5. Which product has the smallest percentage discount?
Proposed correction:
1. Percentage discount for gold bracelet = (Discount / PV) x 100 = (€300 / €2000) x 100 = 15%
2. Percentage discount for diamond necklace = (Discount / PV) x 100 = (€1000 / €5000) x 100 = 20%
3. Percentage discount for silver watch = (Discount / PV) x 100 = (€200 / €1500) x 100 = 13,33%
4. The product with the highest percentage discount is the “Diamond Necklace” with a 20% discount.
5. The product with the smallest percentage discount is the “Silver Watch” with a discount of 13,33%.
Summary of Formulas Used:
– To calculate the percentage discount, the formula is Discount % = (Discount / Sale Price) x 100. We use this formula for the first 3 questions where we calculate the percentage discount for three different products.
– To determine which product has the largest or smallest percentage discount, simply compare the discount percentages of each product and identify the highest and lowest.
All-Star Application
States :
All-Star is a very famous sports shoe store in the city of Marseille. It has a wide range of products intended for top athletes and sports enthusiasts.
All-Star management decides to make a special discount on all products during the summer period in order to boost sales and attract new customers.
The initial price of the SportMax reference shoe is €120 before the discount is applied.
Work to do :
1. If the discount is 15% on the SportMax product, what will be the new price after discount?
2. How much is the discount?
3. If a customer buys 3 pairs of SportMax after the discount, how much would he have paid without the discount?
4. What is the discount percentage if the price of a pair of SportMax goes from €120 to €90?
5. If the store decides to offer an additional 10% discount after applying the first 15% discount on the SportMax product, what will be the price of the pair of SportMax after these two discounts?
Proposed correction:
1. The new price after discount is calculated as follows: Initial price – (Initial price x Ta% discount). In our case: €120 – (€120 x 15/100) = €102.
2. The discount amount is: Initial price x Discount rate. In our case: €120 x 15/100 = €18.
3. Without discount, for 3 pairs of SportMax, the customer would have paid: Initial price x quantity. In our case: €120 x 3 = €360.
4. The discount percentage is calculated using the formula: ((Initial price – Price after discount) / Initial price) x 100. In our case: ((€120 – €90) / €120) x 100 = 25%.
5. To calculate the price after two successive discounts, we proceed step by step. First we apply the first discount of 15% which gives us a price of €102. Then we apply the second discount of 10% on this new price: €102 – (€102 x 10/100) = €91,8.
Summary of Formulas Used:
– New price after discount: Initial price – (Initial price x Discount rate)
– Discount amount: Initial price x Discount rate
– Total without discount: Initial price x Quantity
– Discount percentage: ((Initial price – Price after discount) / Initial price) x 100
– Price after two successive discounts: (Initial price – (Initial price x First discount rate)) – ((Initial price – (Initial price x First discount rate)) x Second discount rate)
High Tech Application
States :
The High Tech company wants to run a promotion on one of its most popular tablets. The initial sale price before discount of the tablet is €499 and the company has decided to apply different discount rates on the product at different times of the promotion.
Work to do :
1. What is the new price after a 15% discount?
2. The company then decides to make a second discount of 10%. What is the new price then?
3. The company then gives a 5% discount on the new price, what is now the final price of the tablet?
4. How much discount in € did the company offer in total since the initial price?
5. What is the total percentage of discounts offered on the initial price?
Proposed correction:
1. The new price after a 15% discount is: €499 – (15/100 x €499) = €424,15.
2. The new price after a second 10% discount is: €424,15 – (10/100 x €424,15) = €381,735.
3. After a 5% discount on the new price, the price of the tablet is: €381,735 – (5/100 x €381,735) = €362,64825.
4. The total discounts offered since the initial price are: €499 – €362,64825 = €136,35175.
5. The total percentage of discounts offered on the initial price is: (€136,35175 / €499) x 100 = 27,32%.
Summary of Formulas Used:
– New price after discount = Initial price – (Discount rate / 100) x Initial price
– Total discounts in € = Initial price – Final price after discounts
– Total discount percentage = (Total discount in € / Initial price) x 100