A Merchant Planned To Sell A Furniture Winning 20 % Of Its Cost; However, He Sold It By Winning 10% Of The Sale Price And, In This Way, He Stopped Receiving 240 Soles For That Sale. Determine The Cost, In Soles, Of The Furniture. A) 2800 B) 3000 C)
A Merchant's Profit Puzzle: Unraveling the Cost of a Furniture Sale
In the world of commerce, profit margins are crucial for a merchant's success. A clever merchant once devised a plan to sell a piece of furniture, aiming to win 20% of its cost. However, he ended up selling it with a 10% profit margin on the sale price, resulting in a loss of 240 soles. In this article, we will delve into the math behind this scenario and determine the cost of the furniture in soles.
Let's break down the problem step by step. The merchant initially planned to sell the furniture with a 20% profit margin on its cost. This means that if the cost price is denoted by 'x', the selling price would be 1.2x (100% + 20% profit margin). However, the merchant ended up selling it with a 10% profit margin on the sale price, which is 1.1 times the sale price.
Let's denote the cost price of the furniture as 'x'. The selling price with a 20% profit margin on the cost would be 1.2x. However, the merchant sold it with a 10% profit margin on the sale price, which is 1.1 times the sale price. This can be represented as:
1.1(1.2x) = x + 240
To find the value of 'x', we need to solve the equation:
1.1(1.2x) = x + 240
Expanding the left-hand side of the equation, we get:
1.32x = x + 240
Subtracting 'x' from both sides of the equation, we get:
0.32x = 240
Dividing both sides of the equation by 0.32, we get:
x = 750
Therefore, the cost of the furniture in soles is 750. This means that the merchant initially planned to sell the furniture at a price of 1.2x = 1.2(750) = 900 soles. However, he ended up selling it at a price of 1.1(900) = 990 soles, resulting in a loss of 240 soles.
This problem requires a deep understanding of algebraic equations and the concept of profit margins. The merchant's initial plan was to sell the furniture with a 20% profit margin on its cost, but he ended up selling it with a 10% profit margin on the sale price. This resulted in a loss of 240 soles. By solving the equation, we were able to determine the cost of the furniture in soles.
The correct answer is:
- a) 750
This is the cost of the furniture in soles.
A Merchant's Profit Puzzle: Unraveling the Cost of a Furniture Sale
In the world of commerce, profit margins are crucial for a merchant's success. A clever merchant once devised a plan to sell a piece of furniture, aiming to win 20% of its cost. However, he ended up selling it with a 10% profit margin on the sale price, resulting in a loss of 240 soles. In this article, we will delve into the math behind this scenario and determine the cost of the furniture in soles.
Let's break down the problem step by step. The merchant initially planned to sell the furniture with a 20% profit margin on its cost. This means that if the cost price is denoted by 'x', the selling price would be 1.2x (100% + 20% profit margin). However, the merchant ended up selling it with a 10% profit margin on the sale price, which is 1.1 times the sale price.
Let's denote the cost price of the furniture as 'x'. The selling price with a 20% profit margin on the cost would be 1.2x. However, the merchant sold it with a 10% profit margin on the sale price, which is 1.1 times the sale price. This can be represented as:
1.1(1.2x) = x + 240
To find the value of 'x', we need to solve the equation:
1.1(1.2x) = x + 240
Expanding the left-hand side of the equation, we get:
1.32x = x + 240
Subtracting 'x' from both sides of the equation, we get:
0.32x = 240
Dividing both sides of the equation by 0.32, we get:
x = 750
Therefore, the cost of the furniture in soles is 750. This means that the merchant initially planned to sell the furniture at a price of 1.2x = 1.2(750) = 900 soles. However, he ended up selling it at a price of 1.1(900) = 990 soles, resulting in a loss of 240 soles.
This problem requires a deep understanding of algebraic equations and the concept of profit margins. The merchant's initial plan was to sell the furniture with a 20% profit margin on its cost, but he ended up selling it with a 10% profit margin on the sale price. This resulted in a loss of 240 soles. By solving the equation, we were able to determine the cost of the furniture in soles.
Q: What is the cost of the furniture in soles? A: The cost of the furniture in soles is 750.
Q: What was the merchant's initial plan for selling the furniture? A: The merchant initially planned to sell the furniture with a 20% profit margin on its cost.
Q: What was the actual profit margin on the sale price? A: The merchant sold the furniture with a 10% profit margin on the sale price.
Q: What was the loss incurred by the merchant? A: The merchant incurred a loss of 240 soles.
Q: How did the merchant's initial plan differ from the actual sale? A: The merchant's initial plan was to sell the furniture at a price of 1.2x, but he ended up selling it at a price of 1.1(900) = 990 soles.
Q: What is the relationship between the cost price and the selling price? A: The selling price is 1.2 times the cost price (100% + 20% profit margin).
Q: How can we represent the relationship between the cost price and the selling price mathematically? A: The relationship can be represented as 1.1(1.2x) = x + 240.
Q: What is the significance of solving the equation 1.1(1.2x) = x + 240? A: Solving the equation allows us to determine the cost of the furniture in soles.
The correct answer is:
- a) 750
This is the cost of the furniture in soles.