A shopkeeper sells two televisions for Rs 1955 each, gaining 15% on one and losing 15% on other. Find his gain or loss percent in the whole transaction.

Options

A. Profit, `2(1/4)` %
B. Profit, 3%
C. Loss, `2(1/4) %`
D. Loss, 3%

Answer

To solve the problem, we need to find the cost price of each television and then calculate the overall gain or loss percentage from selling both televisions.

### Step-by-Step Solution:

1. **Identify the Selling Price (SP)**:
The shopkeeper sells each television for Rs 1955.
\[ SP_1 = SP_2 = 1955 \]

2. **Calculate the Cost Price (CP) for the first television**:
The first television is sold at a gain of 15%.
Let the cost price of the first television be \( CP_1 \).
The formula for selling price when there is a gain is:
\[ SP = CP + \text{Gain} \]
Since Gain = 15% of CP, we can write:
\[ SP_1 = CP_1 + 0.15 \times CP_1 = 1.15 \times CP_1 \]
Rearranging gives:
\[ CP_1 = \frac{SP_1}{1.15} = \frac{1955}{1.15} \approx 1700 \]

3. **Calculate the Cost Price (CP) for the second television**:
The second television is sold at a loss of 15%.
Let the cost price of the second television be \( CP_2 \).
The formula for selling price when there is a loss is:
\[ SP = CP - \text{Loss} \]
Since Loss = 15% of CP, we can write:
\[ SP_2 = CP_2 - 0.15 \times CP_2 = 0.85 \times CP_2 \]
Rearranging gives:
\[ CP_2 = \frac{SP_2}{0.85} = \frac{1955}{0.85} \approx 2300 \]

4. **Calculate the Total Cost Price (CP)**:
Now, we can find the total cost price of both televisions:
\[ CP_{total} = CP_1 + CP_2 = 1700 + 2300 = 4000 \]

5. **Calculate the Total Selling Price (SP)**:
The total selling price of both televisions is:
\[ SP_{total} = SP_1 + SP_2 = 1955 + 1955 = 3910 \]

6. **Calculate Gain or Loss**:
To find the overall gain or loss, we subtract the total cost price from the total selling price:
\[ \text{Loss} = CP_{total} - SP_{total} = 4000 - 3910 = 90 \]

7. **Calculate the Loss Percentage**:
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP_{total}} \right) \times 100 = \left( \frac{90}{4000} \right) \times 100 = 2.25\% \]

### Final Answer:
The shopkeeper incurs a loss of 2.25% in the whole transaction.