A shopkeeper bought 200 arti cles, each costing the same. He sold 30% of the articles at 20% profit and remaining at 10% prof it. If the total profit made by him is 2600, find the cost price of one article.

Options

A. 200
B. 1300
C. 2600
D. 100

Answer

To solve the problem step by step, let's break down the information given and find the cost price of one article.

### Step 1: Understand the total number of articles and their cost price
- The shopkeeper bought **200 articles**.
- Let the cost price of one article be **CP**.

### Step 2: Calculate the total cost price
- The total cost price (CP) for 200 articles is:
\[ \text{Total Cost Price} = 200 \times CP \]

### Step 3: Determine the number of articles sold at different profit percentages
- The shopkeeper sold **30% of the articles** at **20% profit**.
- Number of articles sold at 20% profit:
\[ \text{Articles sold at 20% profit} = 30\% \text{ of } 200 = 0.3 \times 200 = 60 \text{ articles} \]

- The remaining articles sold at **10% profit**:
\[ \text{Remaining articles} = 200 - 60 = 140 \text{ articles} \]

### Step 4: Calculate the selling price for the articles sold at 20% profit
- Selling price (SP) for 60 articles sold at 20% profit:
\[ \text{SP} = \text{CP} \times (1 + \text{Profit Percentage}) = \text{CP} \times (1 + 0.2) = \text{CP} \times 1.2 \]
- Total SP for 60 articles:
\[ \text{Total SP for 60 articles} = 60 \times CP \times 1.2 = 72 \times CP \]

### Step 5: Calculate the selling price for the articles sold at 10% profit
- Selling price for 140 articles sold at 10% profit:
\[ \text{SP} = \text{CP} \times (1 + \text{Profit Percentage}) = \text{CP} \times (1 + 0.1) = \text{CP} \times 1.1 \]
- Total SP for 140 articles:
\[ \text{Total SP for 140 articles} = 140 \times CP \times 1.1 = 154 \times CP \]

### Step 6: Calculate the total selling price
- Total selling price (SP) for all articles:
\[ \text{Total SP} = \text{Total SP for 60 articles} + \text{Total SP for 140 articles} = 72 \times CP + 154 \times CP = 226 \times CP \]

### Step 7: Calculate the total profit
- Total profit is given as **2600**.
- Profit can also be calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
- Therefore:
\[ 2600 = (226 \times CP) - (200 \times CP) \]
\[ 2600 = 26 \times CP \]

### Step 8: Solve for the cost price of one article
- Rearranging the equation gives:
\[ CP = \frac{2600}{26} = 100 \]

### Conclusion
The cost price of one article is **100**.

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