A man sold two watches,each for Rs 495 .If he gained 10% on one watch and suffered a loss of10% on the other, then what is the loss or gain percentage in the transaction?

Options

A. 1% gain
B. 1% loss
C. 100/99% loss
D. Neither gain nor loss

Answer

To solve the problem, we need to determine the cost price of each watch based on the selling price and the gain or loss percentage. Then we can calculate the overall gain or loss percentage for the transaction.

### Step-by-Step Solution:

1. **Determine the Selling Price of Each Watch:**
- Selling Price (SP) of each watch = Rs 495

2. **Calculate the Cost Price (CP) of the First Watch:**
- The first watch is sold at a gain of 10%.
- Let the cost price of the first watch be CP1.
- Using the formula for selling price with gain:
\[ SP = CP + \text{Gain} \]
\[ SP = CP1 + 0.10 \times CP1 = 1.10 \times CP1 \]
- Therefore, we can write:
\[ 495 = 1.10 \times CP1 \]
- Solving for CP1:
\[ CP1 = \frac{495}{1.10} = 450 \]

3. **Calculate the Cost Price (CP) of the Second Watch:**
- The second watch is sold at a loss of 10%.
- Let the cost price of the second watch be CP2.
- Using the formula for selling price with loss:
\[ SP = CP - \text{Loss} \]
\[ SP = CP2 - 0.10 \times CP2 = 0.90 \times CP2 \]
- Therefore, we can write:
\[ 495 = 0.90 \times CP2 \]
- Solving for CP2:
\[ CP2 = \frac{495}{0.90} = 550 \]

4. **Calculate the Total Cost Price and Total Selling Price:**
- Total Cost Price (CP_total) = CP1 + CP2
\[ CP_{total} = 450 + 550 = 1000 \]
- Total Selling Price (SP_total) = SP of first watch + SP of second watch
\[ SP_{total} = 495 + 495 = 990 \]

5. **Calculate Overall Gain or Loss:**
- Overall Loss = Total Cost Price - Total Selling Price
\[ \text{Loss} = CP_{total} - SP_{total} = 1000 - 990 = 10 \]

6. **Calculate Loss Percentage:**
- Loss Percentage = \(\frac{\text{Loss}}{\text{Total Cost Price}} \times 100\)
\[ \text{Loss Percentage} = \frac{10}{1000} \times 100 = 1\% \]

### Final Answer:
The overall loss percentage in the transaction is **1%**.

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