A dealer sold two T.V sets for Rs. 3700 each. On one he gained `10%` and on the other he lost `10%`. The dealer's loss or gain per cent is-

Options

A. `0%`
B. `0.1%`
C. `1%` gain
D. `1%` loss

Answer

To find the overall gain or loss percentage of the dealer from selling the two TV sets, we can follow these steps:

### Step 1: Calculate the Cost Price of Each TV Set
Let the cost price of the first TV set be \( CP_1 \) and the second TV set be \( CP_2 \).

- For the first TV set, the selling price (SP) is Rs. 3700, and the gain is 10%.

\[ SP_1 = CP_1 + 10\% \text{ of } CP_1 = CP_1 + 0.1 \times CP_1 = 1.1 \times CP_1 \]

Therefore, we can express \( CP_1 \) as:

\[ 3700 = 1.1 \times CP_1 \implies CP_1 = \frac{3700}{1.1} = 3363.64 \text{ (approximately)} \]

- For the second TV set, the selling price (SP) is also Rs. 3700, and the loss is 10%.

\[ SP_2 = CP_2 - 10\% \text{ of } CP_2 = CP_2 - 0.1 \times CP_2 = 0.9 \times CP_2 \]

Therefore, we can express \( CP_2 \) as:

\[ 3700 = 0.9 \times CP_2 \implies CP_2 = \frac{3700}{0.9} = 4111.11 \text{ (approximately)} \]

### Step 2: Calculate the Total Cost Price and Total Selling Price
Now, we can calculate the total cost price (TCP) and total selling price (TSP) of both TV sets.

- Total Cost Price (TCP):

\[ TCP = CP_1 + CP_2 = 3363.64 + 4111.11 = 7474.75 \]

- Total Selling Price (TSP):

\[ TSP = SP_1 + SP_2 = 3700 + 3700 = 7400 \]

### Step 3: Calculate the Overall Gain or Loss
Now, we can find the overall gain or loss by comparing the total selling price with the total cost price.

- Loss:

\[ \text{Loss} = TCP - TSP = 7474.75 - 7400 = 74.75 \]

### Step 4: Calculate the Loss Percentage
To find the loss percentage, we use the formula:

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{TCP} \right) \times 100 \]

Substituting the values:

\[ \text{Loss Percentage} = \left( \frac{74.75}{7474.75} \right) \times 100 \approx 1\% \]

### Final Answer
The dealer's loss percentage is approximately **1%**.

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