Two articles were sold for Rs 1199 each. First was sold at 15% loss and second at 15% profit. Find over all profit or loss.

Answer

To find the overall profit or loss from selling two articles, we can follow these steps:

### Step 1: Determine the Selling Price (SP) of Each Article
Both articles are sold for Rs 1199 each.

- Selling Price (SP) of Article 1 = Rs 1199
- Selling Price (SP) of Article 2 = Rs 1199

### Step 2: Calculate the Cost Price (CP) of Each Article
**For Article 1 (sold at 15% loss):**

Let the Cost Price (CP) of Article 1 be \( CP_1 \).

Since it is sold at a 15% loss:
\[ SP = CP_1 - (15\% \text{ of } CP_1) = CP_1 \times \left(1 - \frac{15}{100}\right) = CP_1 \times 0.85 \]
Setting this equal to the selling price:
\[ 1199 = CP_1 \times 0.85 \]
To find \( CP_1 \):
\[ CP_1 = \frac{1199}{0.85} = 1410.59 \text{ (approximately)} \]

**For Article 2 (sold at 15% profit):**

Let the Cost Price (CP) of Article 2 be \( CP_2 \).

Since it is sold at a 15% profit:
\[ SP = CP_2 + (15\% \text{ of } CP_2) = CP_2 \times \left(1 + \frac{15}{100}\right) = CP_2 \times 1.15 \]
Setting this equal to the selling price:
\[ 1199 = CP_2 \times 1.15 \]
To find \( CP_2 \):
\[ CP_2 = \frac{1199}{1.15} = 1042.61 \text{ (approximately)} \]

### Step 3: Calculate the Total Cost Price (CP) and Total Selling Price (SP)
- Total CP = \( CP_1 + CP_2 \)
\[ Total \, CP = 1410.59 + 1042.61 = 2453.20 \]

- Total SP = \( SP_1 + SP_2 \)
\[ Total \, SP = 1199 + 1199 = 2398 \]

### Step 4: Determine Overall Profit or Loss
To find the overall profit or loss:
\[ Overall \, Profit/Loss = Total \, SP - Total \, CP \]
\[ Overall \, Profit/Loss = 2398 - 2453.20 = -55.20 \]

Since the result is negative, it indicates a loss.

### Step 5: Calculate the Percentage of Loss
To find the percentage of loss:
\[ \text{Percentage of Loss} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 \]
\[ \text{Percentage of Loss} = \left(\frac{55.20}{2453.20}\right) \times 100 \approx 2.25\% \]

### Final Answer
The overall loss is approximately **Rs 55.20**, which is about **2.25%**.

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