Greg sell two watches for $ 1955 each gaining 15% on one and losing 15% on the other. Find her gain or loss per cent in the whole trasaction.

Answer

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

### Step-by-Step Solution:

1. **Identify the Selling Price (SP) of Each Watch:**
- SP of the first watch = $1955
- SP of the second watch = $1955

2. **Calculate the Cost Price (CP) of the First Watch:**
- Gain = 15%
- Formula to find CP when SP and gain percentage are known:
\[ CP = \frac{SP \times 100}{100 + \text{Gain \%}} \]
- Plugging in the values:
\[ CP_1 = \frac{1955 \times 100}{100 + 15} = \frac{1955 \times 100}{115} = 1700 \]

3. **Calculate the Cost Price (CP) of the Second Watch:**
- Loss = 15%
- Formula to find CP when SP and loss percentage are known:
\[ CP = \frac{SP \times 100}{100 - \text{Loss \%}} \]
- Plugging in the values:
\[ CP_2 = \frac{1955 \times 100}{100 - 15} = \frac{1955 \times 100}{85} = 2300 \]

4. **Calculate the Total Cost Price (CP) of Both Watches:**
- Total CP = CP of first watch + CP of second watch
\[ \text{Total CP} = 1700 + 2300 = 4000 \]

5. **Calculate the Total Selling Price (SP) of Both Watches:**
- Total SP = SP of first watch + SP of second watch
\[ \text{Total SP} = 1955 + 1955 = 3910 \]

6. **Determine the Overall Gain or Loss:**
- Since Total SP < Total CP, there is a loss.
- Loss = Total CP - Total SP
\[ \text{Loss} = 4000 - 3910 = 90 \]

7. **Calculate the Loss Percentage:**
- Formula for loss percentage:
\[ \text{Loss \%} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 \]
- Plugging in the values:
\[ \text{Loss \%} = \left(\frac{90}{4000}\right) \times 100 = 2.25\% \]

### Final Answer:
Greg incurred a loss of **2.25%** in the whole transaction.

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