To solve the problem, we need to determine the total gain or loss when Kewal sells two tape recorders at the same selling price (SP) but with different profit and loss percentages.
### Step-by-step Solution:
1. **Understanding the Selling Price (SP)**:
Let the selling price of each tape recorder be \( SP \).
2. **Calculating the Cost Price (CP) for each tape recorder**:
- For the first tape recorder, Kewal gains 10%.
- Let the cost price of the first tape recorder be \( CP_1 \).
- The selling price can be expressed as:
\[
SP = CP_1 + 0.10 \times CP_1 = 1.10 \times CP_1
\]
- Therefore, we can express \( CP_1 \) in terms of \( SP \):
\[
CP_1 = \frac{SP}{1.10}
\]
- For the second tape recorder, Kewal loses 10%.
- Let the cost price of the second tape recorder be \( CP_2 \).
- The selling price can be expressed as:
\[
SP = CP_2 - 0.10 \times CP_2 = 0.90 \times CP_2
\]
- Therefore, we can express \( CP_2 \) in terms of \( SP \):
\[
CP_2 = \frac{SP}{0.90}
\]
3. **Calculating Total Cost Price (CP)**:
- The total cost price for both tape recorders is:
\[
Total \, CP = CP_1 + CP_2 = \frac{SP}{1.10} + \frac{SP}{0.90}
\]
4. **Finding a Common Denominator**:
- To add these fractions, we find a common denominator, which is \( 1.10 \times 0.90 = 0.99 \).
- Thus, we rewrite the fractions:
\[
Total \, CP = \frac{SP \times 0.90}{0.99} + \frac{SP \times 1.10}{0.99} = \frac{0.90SP + 1.10SP}{0.99} = \frac{2.00SP}{0.99}
\]
5. **Calculating Total Selling Price (SP)**:
- The total selling price for both tape recorders is:
\[
Total \, SP = SP + SP = 2SP
\]
6. **Calculating Total Gain or Loss**:
- Now, we can find the total gain or loss:
\[
Total \, Gain/Loss = Total \, SP - Total \, CP = 2SP - \frac{2.00SP}{0.99}
\]
- To simplify:
\[
Total \, Gain/Loss = 2SP \left(1 - \frac{2.00}{0.99}\right) = 2SP \left(\frac{0.99 - 2.00}{0.99}\right) = 2SP \left(\frac{-1.01}{0.99}\right)
\]
- This indicates a loss.
7. **Calculating the Percentage of Loss**:
- The percentage of loss can be calculated as:
\[
Loss \% = \left(\frac{Total \, Loss}{Total \, CP}\right) \times 100
\]
- Since we have established that the total loss is \( 2SP \times \frac{1.01}{0.99} \), we can find the percentage:
\[
Loss \% = \frac{1.01}{2} \times 100 \approx 1\%
\]
### Final Conclusion:
Kewal experiences a total loss of approximately **1%** in the transaction.
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