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 step by step, let's follow the process of calculating the overall gain or loss percentage from the transactions involving the two watches.

### Step 1: Understand the Selling Price
Greg sells two watches for $1955 each. Therefore, the selling price (SP) of each watch is:
- SP of Watch 1 = $1955
- SP of Watch 2 = $1955

### Step 2: Calculate the Cost Price for Each Watch
Let’s denote the cost price (CP) of Watch 1 as CP1 and the cost price of Watch 2 as CP2.

For Watch 1, Greg gains 15%. This means:
- Selling Price (SP) = Cost Price (CP) + Gain
- Gain = 15% of CP1 = (15/100) * CP1

Using the formula for SP:
\[ SP1 = CP1 + \left(\frac{15}{100} \times CP1\right) \]
\[ 1955 = CP1 + 0.15 \times CP1 \]
\[ 1955 = 1.15 \times CP1 \]
\[ CP1 = \frac{1955}{1.15} \]
\[ CP1 = 1700 \]

For Watch 2, Greg loses 15%. This means:
- Selling Price (SP) = Cost Price (CP) - Loss
- Loss = 15% of CP2 = (15/100) * CP2

Using the formula for SP:
\[ SP2 = CP2 - \left(\frac{15}{100} \times CP2\right) \]
\[ 1955 = CP2 - 0.15 \times CP2 \]
\[ 1955 = 0.85 \times CP2 \]
\[ CP2 = \frac{1955}{0.85} \]
\[ CP2 = 2300 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now, we can calculate the total cost price (TCP) and total selling price (TSP) for both watches.
- Total Cost Price (TCP) = CP1 + CP2
\[ TCP = 1700 + 2300 = 4000 \]

- Total Selling Price (TSP) = SP1 + SP2
\[ TSP = 1955 + 1955 = 3910 \]

### Step 4: Calculate Overall Gain or Loss
Now, we can determine whether there is a gain or a loss:
- Loss = TCP - TSP
\[ Loss = 4000 - 3910 = 90 \]

### Step 5: Calculate Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total Cost Price}} \times 100\right) \]
\[ \text{Loss Percentage} = \left(\frac{90}{4000} \times 100\right) \]
\[ \text{Loss Percentage} = 2.25\% \]

### Final Answer
Greg incurs a loss of 2.25% in the whole transaction.

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