A man sells two items at Rs. 250 each. What is the value of (in Rs.) of the profit or loss incurred in this transaction. If he sells one at a profit of 25% and the other at a loss of 25%.

Options

A. Profit, 33.33
B. Profit, 66.67
C. Loss, 66.67
D. Loss, 33.33

Answer

To solve the problem, we need to determine the cost price (CP) of each item and then find the total cost price to calculate the overall profit or loss incurred in the transaction.

### Step-by-Step Solution:

1. **Identify Selling Price (SP) for both items:**
- Selling Price of Item 1 (SP1) = Rs. 250
- Selling Price of Item 2 (SP2) = Rs. 250
- Total Selling Price (SP) = SP1 + SP2 = 250 + 250 = Rs. 500

2. **Calculate Cost Price (CP) of Item 1:**
- Item 1 is sold at a profit of 25%.
- Let the Cost Price of Item 1 be CP1.
- We know that Selling Price = Cost Price + Profit
- Profit = 25% of CP1 = (25/100) * CP1 = 0.25 * CP1
- Therefore, SP1 = CP1 + 0.25 * CP1 = 1.25 * CP1
- Rearranging gives us: CP1 = SP1 / 1.25 = 250 / 1.25 = Rs. 200

3. **Calculate Cost Price (CP) of Item 2:**
- Item 2 is sold at a loss of 25%.
- Let the Cost Price of Item 2 be CP2.
- Selling Price = Cost Price - Loss
- Loss = 25% of CP2 = (25/100) * CP2 = 0.25 * CP2
- Therefore, SP2 = CP2 - 0.25 * CP2 = 0.75 * CP2
- Rearranging gives us: CP2 = SP2 / 0.75 = 250 / 0.75 = Rs. 333.33

4. **Calculate Total Cost Price (CP):**
- Total CP = CP1 + CP2 = 200 + 333.33 = Rs. 533.33

5. **Calculate Profit or Loss:**
- Total Selling Price (SP) = Rs. 500
- Total Cost Price (CP) = Rs. 533.33
- Loss = Total CP - Total SP = 533.33 - 500 = Rs. 33.33

### Conclusion:
The man incurs a loss of Rs. 33.33 in this transaction.

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