A man sold two watches for Rs. 1000 each. On one he gains 25% and on the other 20% loss. Find how much % does he gain or lose in the whole transaction?

Options

A. `(100)/(41)%` loss
B. `(100)/(41)%` gain
C. No gain, no loss
D. Cannot be determined

Answer

To solve the problem step by step, we need to calculate the cost price (CP) of each watch based on the given selling price (SP) and the gain or loss percentage. Then, we will find the total cost price and total selling price to determine the overall gain or loss percentage.

### Step 1: Calculate the Cost Price of the First Watch
- **Selling Price (SP1)** = Rs. 1000
- **Gain Percentage** = 25%

Using the formula for cost price when there is a gain:
\[ CP = \frac{100 \times SP}{100 + \text{Gain Percentage}} \]
Substituting the values:
\[ CP1 = \frac{100 \times 1000}{100 + 25} = \frac{100000}{125} = 800 \]

### Step 2: Calculate the Cost Price of the Second Watch
- **Selling Price (SP2)** = Rs. 1000
- **Loss Percentage** = 20%

Using the formula for cost price when there is a loss:
\[ CP = \frac{100 \times SP}{100 - \text{Loss Percentage}} \]
Substituting the values:
\[ CP2 = \frac{100 \times 1000}{100 - 20} = \frac{100000}{80} = 1250 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
- **Total Cost Price (CP)** = CP1 + CP2
\[ Total CP = 800 + 1250 = 2050 \]

- **Total Selling Price (SP)** = SP1 + SP2
\[ Total SP = 1000 + 1000 = 2000 \]

### Step 4: Calculate the Overall Gain or Loss
- **Loss** = Total CP - Total SP
\[ Loss = 2050 - 2000 = 50 \]

### Step 5: Calculate the Percentage of Loss
Using the formula for percentage loss:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{50}{2050} \right) \times 100 \approx 2.44\% \]

### Final Answer
The man incurs an overall loss of approximately **2.44%** in the whole transaction.

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