A person bought some caps at rate of 27 for Rs 102 and sold them at the rate of 8 for Rs 34. Find the profit or loss %.

Answer

To solve the problem, we will calculate the cost price (CP) and selling price (SP) of the caps, then determine the profit or loss percentage.

### Step-by-step Solution:

1. **Calculate the Cost Price (CP) of one cap:**
- The person bought 27 caps for Rs. 102.
- Therefore, the cost price of one cap (CP) is calculated as:
\[ CP = \frac{102}{27} \approx 3.78 \text{ Rs.} \]

2. **Calculate the Selling Price (SP) of one cap:**
- The person sold 8 caps for Rs. 34.
- Therefore, the selling price of one cap (SP) is calculated as:
\[ SP = \frac{34}{8} = 4.25 \text{ Rs.} \]

3. **Determine the Profit or Loss:**
- To find the profit, subtract the cost price from the selling price:
\[ \text{Profit} = SP - CP = 4.25 - 3.78 = 0.47 \text{ Rs.} \]

4. **Calculate the Profit Percentage:**
- The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
- Plugging in the values:
\[ \text{Profit Percentage} = \left( \frac{0.47}{3.78} \right) \times 100 \approx 12.43\% \]

5. **Final Answer:**
- The profit percentage is approximately **12.43%**.