A man sells two wrist watches one at a profit of 10% and another at a loss of 10%, but the selling price of each watch is Rs. 200. Find the :
(1) percentage profit or loss.
(2) net amount of profit or loss.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Selling Prices and Profit/Loss Percentages
We have two wrist watches:
- Watch 1 is sold at a profit of 10%.
- Watch 2 is sold at a loss of 10%.
Both watches are sold for Rs. 200 each.

### Step 2: Calculate the Cost Price (CP) for Watch 1
The selling price (SP) of Watch 1 is Rs. 200.
Since there is a profit of 10%, we can use the formula:
\[ SP = CP + \text{Profit} \]
Where Profit is 10% of CP. Therefore, we can write:
\[ SP = CP + 0.10 \times CP = 1.10 \times CP \]
So,
\[ 200 = 1.10 \times CP \]
To find CP, we rearrange the equation:
\[ CP = \frac{200}{1.10} = \frac{2000}{11} \approx 181.82 \]

### Step 3: Calculate the Cost Price (CP) for Watch 2
For Watch 2, the selling price is also Rs. 200, but it is sold at a loss of 10%.
Using the formula:
\[ SP = CP - \text{Loss} \]
Where Loss is 10% of CP. Thus:
\[ SP = CP - 0.10 \times CP = 0.90 \times CP \]
So,
\[ 200 = 0.90 \times CP \]
Rearranging gives:
\[ CP = \frac{200}{0.90} = \frac{2000}{9} \approx 222.22 \]

### Step 4: Calculate Total Cost Price (CP) and Total Selling Price (SP)
Now we can find the total CP and total SP:
- Total CP = CP of Watch 1 + CP of Watch 2
\[ Total\ CP = \frac{2000}{11} + \frac{2000}{9} \]
To add these fractions, we need a common denominator:
The least common multiple of 11 and 9 is 99.
\[ Total\ CP = \frac{2000 \times 9}{99} + \frac{2000 \times 11}{99} = \frac{18000 + 22000}{99} = \frac{40000}{99} \approx 404.04 \]

- Total SP = SP of Watch 1 + SP of Watch 2
\[ Total\ SP = 200 + 200 = 400 \]

### Step 5: Calculate Net Profit or Loss
Now, we can find the net profit or loss:
\[ Net\ Profit/Loss = Total\ SP - Total\ CP \]
\[ Net\ Profit/Loss = 400 - \frac{40000}{99} \]
To calculate this, we convert 400 into a fraction with a denominator of 99:
\[ 400 = \frac{39600}{99} \]
So,
\[ Net\ Profit/Loss = \frac{39600}{99} - \frac{40000}{99} = \frac{-400}{99} \]
This indicates a loss of Rs. 4.04 (approximately).

### Step 6: Calculate Percentage Loss
To find the percentage loss:
\[ Percentage\ Loss = \left( \frac{Net\ Loss}{Total\ CP} \right) \times 100 \]
\[ Percentage\ Loss = \left( \frac{400/99}{40000/99} \right) \times 100 = \left( \frac{400}{40000} \right) \times 100 = 1\% \]

### Final Answers:
1. **Percentage Loss**: 1%
2. **Net Amount of Loss**: Rs. 4.04 (approximately)