To solve the problem, we need to find the overall profit or loss percentage when two articles are sold at the same selling price. Here’s a step-by-step solution:
### Step 1: Identify the Selling Price
The selling price (SP) of both articles is given as Rs. 10,591.
### Step 2: Calculate the Cost Price of the First Article
The first article is sold at a profit of 19%. We can use the formula for selling price:
\[
SP = CP + \text{Profit}
\]
Where Profit can be calculated as:
\[
\text{Profit} = \frac{19}{100} \times CP_1
\]
Substituting this into the selling price formula gives us:
\[
10,591 = CP_1 + \frac{19}{100} \times CP_1
\]
This can be simplified to:
\[
10,591 = CP_1 \left(1 + \frac{19}{100}\right)
\]
\[
10,591 = CP_1 \left(\frac{119}{100}\right)
\]
Now, we can solve for \(CP_1\):
\[
CP_1 = \frac{10,591 \times 100}{119}
\]
Calculating this gives:
\[
CP_1 \approx 8,900
\]
### Step 3: Calculate the Cost Price of the Second Article
The second article is sold at a loss of 11%. Using the same selling price formula:
\[
SP = CP - \text{Loss}
\]
Where Loss can be calculated as:
\[
\text{Loss} = \frac{11}{100} \times CP_2
\]
Substituting this into the selling price formula gives us:
\[
10,591 = CP_2 - \frac{11}{100} \times CP_2
\]
This can be simplified to:
\[
10,591 = CP_2 \left(1 - \frac{11}{100}\right)
\]
\[
10,591 = CP_2 \left(\frac{89}{100}\right)
\]
Now, we can solve for \(CP_2\):
\[
CP_2 = \frac{10,591 \times 100}{89}
\]
Calculating this gives:
\[
CP_2 \approx 11,900
\]
### Step 4: Calculate Total Cost Price
Now, we can find the total cost price (CP) of both articles:
\[
\text{Total CP} = CP_1 + CP_2 = 8,900 + 11,900 = 20,800
\]
### Step 5: Calculate Total Selling Price
The total selling price (SP) of both articles is:
\[
\text{Total SP} = 10,591 + 10,591 = 21,182
\]
### Step 6: Calculate Overall Profit or Loss
Now, we can find the overall profit or loss:
\[
\text{Total Profit} = \text{Total SP} - \text{Total CP} = 21,182 - 20,800 = 382
\]
### Step 7: Calculate Profit Percentage
Finally, we calculate the profit percentage:
\[
\text{Profit Percentage} = \left(\frac{\text{Total Profit}}{\text{Total CP}}\right) \times 100
\]
Substituting the values gives:
\[
\text{Profit Percentage} = \left(\frac{382}{20,800}\right) \times 100 \approx 1.83\%
\]
### Conclusion
The overall profit percentage is approximately **1.83%**.
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