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Sagot :
Sure, let's break down the details of the problem step-by-step.
Step 1: Understanding the problem statement
- The businessman buys two horses.
- He gains 10% on the first horse and loses 10% on the second horse.
- We need to find the overall percentage of gain or loss on the entire deal.
Step 2: Assume the cost price for each horse
To simplify calculations, let's assume the cost price of each horse is [tex]$100. Thus: - Cost price of the first horse (CP₁) = $[/tex]100
- Cost price of the second horse (CP₂) = [tex]$100 Step 3: Calculate the selling price of the first horse Since the businessman gains 10% on the first horse: - Selling price of the first horse (SP₁) = CP₁ + 10% of CP₁ - SP₁ = 100 + (10/100) × 100 - SP₁ = 100 + 10 - SP₁ = $[/tex]110
Step 4: Calculate the selling price of the second horse
Since the businessman loses 10% on the second horse:
- Selling price of the second horse (SP₂) = CP₂ - 10% of CP₂
- SP₂ = 100 - (10/100) × 100
- SP₂ = 100 - 10
- SP₂ = [tex]$90 Step 5: Calculate the total cost price and the total selling price - Total cost price (TCP) = CP₁ + CP₂ - TCP = 100 + 100 - TCP = $[/tex]200
- Total selling price (TSP) = SP₁ + SP₂
- TSP = 110 + 90
- TSP = [tex]$200 Step 6: Determine the overall gain or loss In this case, since the total cost price (TCP) is equal to the total selling price (TSP): - Overall gain or loss = TSP - TCP - Overall gain or loss = 200 - 200 - Overall gain or loss = $[/tex]0
Step 7: Calculate the percentage of overall gain or loss
Since there is no overall gain or loss, the percentage of overall gain or loss is:
- Gain or loss percentage = (Overall gain or loss / TCP) × 100
- Gain or loss percentage = (0 / 200) × 100
- Gain or loss percentage = 0%
So, the businessman does not have any overall gain or loss in this deal.
Therefore, the overall pecentage of gain or loss in the entire deal is 0%.
Step 1: Understanding the problem statement
- The businessman buys two horses.
- He gains 10% on the first horse and loses 10% on the second horse.
- We need to find the overall percentage of gain or loss on the entire deal.
Step 2: Assume the cost price for each horse
To simplify calculations, let's assume the cost price of each horse is [tex]$100. Thus: - Cost price of the first horse (CP₁) = $[/tex]100
- Cost price of the second horse (CP₂) = [tex]$100 Step 3: Calculate the selling price of the first horse Since the businessman gains 10% on the first horse: - Selling price of the first horse (SP₁) = CP₁ + 10% of CP₁ - SP₁ = 100 + (10/100) × 100 - SP₁ = 100 + 10 - SP₁ = $[/tex]110
Step 4: Calculate the selling price of the second horse
Since the businessman loses 10% on the second horse:
- Selling price of the second horse (SP₂) = CP₂ - 10% of CP₂
- SP₂ = 100 - (10/100) × 100
- SP₂ = 100 - 10
- SP₂ = [tex]$90 Step 5: Calculate the total cost price and the total selling price - Total cost price (TCP) = CP₁ + CP₂ - TCP = 100 + 100 - TCP = $[/tex]200
- Total selling price (TSP) = SP₁ + SP₂
- TSP = 110 + 90
- TSP = [tex]$200 Step 6: Determine the overall gain or loss In this case, since the total cost price (TCP) is equal to the total selling price (TSP): - Overall gain or loss = TSP - TCP - Overall gain or loss = 200 - 200 - Overall gain or loss = $[/tex]0
Step 7: Calculate the percentage of overall gain or loss
Since there is no overall gain or loss, the percentage of overall gain or loss is:
- Gain or loss percentage = (Overall gain or loss / TCP) × 100
- Gain or loss percentage = (0 / 200) × 100
- Gain or loss percentage = 0%
So, the businessman does not have any overall gain or loss in this deal.
Therefore, the overall pecentage of gain or loss in the entire deal is 0%.
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