Profit and Loss in Buying and Selling ③ Profit and Loss on Two Types of Goods
Problems that ask, “When two types of goods are sold together, how much is the total profit or loss?” are common application problems in junior high school entrance examinations.
The key is to consider the profit on one type together with the loss on the other type.
What You Will Learn
When there is “a profit of 〇 yen on A and a loss of 〇 yen on B,” calculate the overall profit or loss = amount for A ＋ amount for B.
In problems involving the sale of many goods, the trick is to calculate “profit per item × number of items” for each product and then add the results together.
Example Problem
A shop bought 100 apples. Of these, 80 were sold at 20% above cost, and the remaining 20 were sold at 10% below cost. If the cost of one apple was 50 yen, how much was the total profit?
Solution:
① Calculate the profit on the 80 apples.
Selling price: 50 × 1.2 ＝ 60 yen
Profit per item: 60 － 50 ＝ 10 yen
Profit on 80 items: 10 × 80 ＝ 800 yen
② Calculate the loss on the 20 apples.
Selling price: 50 × 0.9 ＝ 45 yen
Loss per item: 50 － 45 ＝ 5 yen
Loss on 20 items: 5 × 20 ＝ 100 yen
③ Total profit ＝ 800 － 100 ＝ 700 yen
A shop bought 100 apples. Of these, 80 were sold at 20% above cost, and the remaining 20 were sold at 10% below cost. If the cost of one apple was 50 yen, how much was the total profit?
Solution:
① Calculate the profit on the 80 apples.
Selling price: 50 × 1.2 ＝ 60 yen
Profit per item: 60 － 50 ＝ 10 yen
Profit on 80 items: 10 × 80 ＝ 800 yen
② Calculate the loss on the 20 apples.
Selling price: 50 × 0.9 ＝ 45 yen
Loss per item: 50 － 45 ＝ 5 yen
Loss on 20 items: 5 × 20 ＝ 100 yen
③ Total profit ＝ 800 － 100 ＝ 700 yen
Key Points
Remember
- When there are many types of goods, “calculate the profit or loss for each product and then add them together.”
- A loss can be handled by “subtracting” it from the total profit.
- Summarizing the information in a table before calculating makes it less likely that you will make a mistake.
Practice Problems
- Product A (cost price 400 yen) was sold at a 30% markup, and Product B (cost price 600 yen) was sold at a 20% discount. Find the profit (or loss) on each of A and B, and the combined amount.
- Of 50 items purchased, 40 were sold at 30% above cost and 10 were sold at 10% below cost. If the total profit was 2000 yen, find the cost price of one item.
Answers and Explanations
- Answer: Profit on A = 120 yen, loss on B = 120 yen, total profit or loss = ±0 yen (no profit or loss)
Explanation: Selling price of A = 400 × 1.3 = 520 yen. Profit on A = 520 − 400 = 120 yen. Selling price of B = 600 × 0.8 = 480 yen. Loss on B = 600 − 480 = 120 yen. Total = 120 − 120 = 0 yen (neither a profit nor a loss). - Answer: Cost price of one item = 2000/11 yen (approximately 181.8 yen)
Explanation: Let the cost price be x yen. The profit from selling 40 items at 30% above cost is 0.3x × 40 = 12x. The loss from selling 10 items at 10% below cost is 0.1x × 10 = x. Since the total profit was 2000 yen, 12x－x＝2000. Therefore, 11x＝2000, so x＝2000/11 yen (approximately 181.8 yen).