Gurpreet sells two watches for Rs.2970 each, gaining 10% on one and losing 10% on the other. Find her gain or loss percent in the whole transaction.

Answer

To solve the problem step by step, we will calculate the cost price (CP) of each watch, the total cost price, the total selling price (SP), and finally determine the overall gain or loss percentage.

### Step 1: Calculate the Cost Price of the First Watch
- Selling Price (SP) of the first watch = Rs. 2970
- Gain percentage = 10%

Using the formula for cost price when there is a gain:
\[ CP = \frac{100}{100 + \text{Gain \%}} \times SP \]
Substituting the values:
\[ CP_1 = \frac{100}{100 + 10} \times 2970 = \frac{100}{110} \times 2970 \]
Calculating:
\[ CP_1 = \frac{100 \times 2970}{110} = \frac{297000}{110} = 2700 \]

### Step 2: Calculate the Cost Price of the Second Watch
- Selling Price (SP) of the second watch = Rs. 2970
- Loss percentage = 10%

Using the formula for cost price when there is a loss:
\[ CP = \frac{100}{100 - \text{Loss \%}} \times SP \]
Substituting the values:
\[ CP_2 = \frac{100}{100 - 10} \times 2970 = \frac{100}{90} \times 2970 \]
Calculating:
\[ CP_2 = \frac{100 \times 2970}{90} = \frac{297000}{90} = 3300 \]

### Step 3: Calculate the Total Cost Price
Now, we will find the total cost price of both watches:
\[ \text{Total CP} = CP_1 + CP_2 = 2700 + 3300 = 6000 \]

### Step 4: Calculate the Total Selling Price
Now, we will find the total selling price of both watches:
\[ \text{Total SP} = SP_1 + SP_2 = 2970 + 2970 = 5940 \]

### Step 5: Calculate the Overall Gain or Loss
Now we will find the overall gain or loss:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 6000 - 5940 = 60 \]

### Step 6: Calculate the Loss Percentage
Finally, we will calculate the loss percentage using the formula:
\[ \text{Loss \%} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss \%} = \left( \frac{60}{6000} \right) \times 100 = 1\% \]

### Final Answer
Gurpreet incurred a loss of 1% in the whole transaction.

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