Profit and Loss in Buying and Selling ① The Relationship Between Cost Price, List Price, and Selling Price
When buying and selling goods in a store, three types of “prices” appear.
① The price the store paid to purchase the product (cost price), ② the price the store decided to sell it for (list price), and ③ the price at which it was actually sold (selling price).
Let us organize the relationship among these three prices carefully.
What You Will Learn
Cost price: The amount of money the store paid to purchase a product (also called the purchase price)
List price: The price set by the store by adding a profit to the cost price
Selling price: The price at which the product was actually sold. It may be discounted from the list price
Profit: The amount earned. Profit = Selling price − Cost price
Example Problem
A product with a cost price of 2,000 yen was given a list price by adding a profit of 30% of the cost price. What is the list price? Furthermore, if the product is sold at a 10% discount from the list price, how much profit will be made?
Solution:
① Calculate the list price.
List price = 2000 ×（1 ＋ 0.3）＝ 2000 × 1.3 ＝ 2600 yen
② Calculate the selling price (a 10% discount means multiplying by 0.9).
Selling price = 2600 ×（1 － 0.1）＝ 2600 × 0.9 ＝ 2340 yen
③ Profit = Selling price − Cost price = 2340 － 2000 ＝ 340 yen
A product with a cost price of 2,000 yen was given a list price by adding a profit of 30% of the cost price. What is the list price? Furthermore, if the product is sold at a 10% discount from the list price, how much profit will be made?
Solution:
① Calculate the list price.
List price = 2000 ×（1 ＋ 0.3）＝ 2000 × 1.3 ＝ 2600 yen
② Calculate the selling price (a 10% discount means multiplying by 0.9).
Selling price = 2600 ×（1 － 0.1）＝ 2600 × 0.9 ＝ 2340 yen
③ Profit = Selling price − Cost price = 2340 － 2000 ＝ 340 yen
Key Points
Remember
- List price = Cost price ×（1 ＋ Profit rate）
- Selling price = List price ×（1 － Discount rate）
- Profit = Selling price − Cost price (If the result is negative, it means that a loss was made.)
Practice Problems
- A product with a cost price of 1,500 yen was given a list price by adding a profit of 40%. What is the list price?
- A product with a list price of 3,000 yen was sold at a 20% discount. What is the selling price?
- A product with a cost price of 800 yen was sold at a 25% discount from its list price, resulting in a profit of 100 yen. What was the list price?
Answers and Explanations
- Answer: List price = 2,100 yen
Explanation: List price = Cost price × (1 + Profit rate) = 1500 × 1.4 = 2100 yen. - Answer: Selling price = 2,400 yen
Explanation: A 20% discount means subtracting 20% of the list price. Selling price = 3000 × (1 − 0.2) = 3000 × 0.8 = 2400 yen. - Answer: List price = 1,200 yen
Explanation: Selling price = Cost price + Profit = 800 + 100 = 900 yen. The selling price is 25% below the list price = List price × 0.75, so List price = 900 ÷ 0.75 = 1200 yen.