Selling price offirst article is Rs 470 and costprice of second article is Rs 470. If there is a loss of 20% onfirst article and profit of 20% on secondarticle, then what will be the overall profit or loss percentage?

Options

A. 2.22% loss
B. 4% profit
C. No profit no loss
D. 1.80% loss

Answer

To solve the problem step-by-step, we will calculate the cost price of the first article, the selling price of the second article, and then determine the overall profit or loss percentage.

### Step 1: Calculate the Cost Price of the First Article
Given that the selling price (SP) of the first article is Rs 470 and there is a loss of 20%, we can find the cost price (CP) using the formula:

\[ \text{SP} = \text{CP} \times (1 - \text{Loss Percentage}) \]

Substituting the values:

\[ 470 = \text{CP} \times (1 - 0.20) \]

\[ 470 = \text{CP} \times 0.80 \]

Now, solving for CP:

\[ \text{CP} = \frac{470}{0.80} = 587.5 \]

### Step 2: Calculate the Selling Price of the Second Article
Given that the cost price of the second article is Rs 470 and there is a profit of 20%, we can find the selling price (SP) using the formula:

\[ \text{SP} = \text{CP} \times (1 + \text{Profit Percentage}) \]

Substituting the values:

\[ \text{SP} = 470 \times (1 + 0.20) \]

\[ \text{SP} = 470 \times 1.20 = 564 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now, we can calculate the total cost price (CP) and total selling price (SP) for both articles.

- Total Cost Price (CP):
\[ \text{Total CP} = \text{CP of First Article} + \text{CP of Second Article} = 587.5 + 470 = 1057.5 \]

- Total Selling Price (SP):
\[ \text{Total SP} = \text{SP of First Article} + \text{SP of Second Article} = 470 + 564 = 1034 \]

### Step 4: Calculate Overall Profit or Loss
To find out whether there is an overall profit or loss, we subtract the total selling price from the total cost price:

\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 1057.5 - 1034 = 23.5 \]

### Step 5: Calculate Loss Percentage
Finally, we can calculate the loss percentage using the formula:

\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 \]

Substituting the values:

\[ \text{Loss Percentage} = \left(\frac{23.5}{1057.5}\right) \times 100 \approx 2.22\% \]

### Conclusion
The overall loss percentage is approximately **2.22%**.

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