A man sold two TV sets for Rs 7.200 each, neither incurring a gain nor a loss. If he sold one TV set at a profit of `12(1)/(2)%`, then the other TV set is sold at a loss of

Options

A. `8.5%`
B. `9%`
C. `8%`
D. `10%`

Answer

To solve the problem step by step, we need to find out the loss percentage incurred on the second TV set after selling the first TV set at a profit of 12.5%.

### Step 1: Understand the Selling Price
The man sold both TV sets for Rs 7,200 each. Therefore, the selling price (SP) of each TV set is:
\[ SP_1 = SP_2 = 7200 \]

### Step 2: Calculate the Cost Price of the First TV Set
The first TV set was sold at a profit of 12.5%. To find the cost price (CP) of the first TV set, we can use the formula for selling price with profit:
\[ SP = CP + \text{Profit} \]
Where profit can be expressed as:
\[ \text{Profit} = \frac{12.5}{100} \times CP \]
This can also be written as:
\[ SP = CP \left(1 + \frac{12.5}{100}\right) = CP \times 1.125 \]

Now substituting the selling price:
\[ 7200 = CP_1 \times 1.125 \]
To find \( CP_1 \):
\[ CP_1 = \frac{7200}{1.125} \]

### Step 3: Calculate CP_1
Calculating \( CP_1 \):
\[ CP_1 = \frac{7200}{1.125} = 6400 \]

### Step 4: Determine Total Cost Price
Since there is neither a gain nor a loss overall, the total cost price of both TV sets is equal to the total selling price:
\[ CP_1 + CP_2 = SP_1 + SP_2 \]
\[ 6400 + CP_2 = 7200 + 7200 \]
\[ 6400 + CP_2 = 14400 \]

### Step 5: Calculate CP_2
Now, we can find \( CP_2 \):
\[ CP_2 = 14400 - 6400 = 8000 \]

### Step 6: Calculate the Loss on the Second TV Set
The second TV set was sold for Rs 7,200, but its cost price was Rs 8,000. Therefore, the loss incurred on the second TV set is:
\[ \text{Loss} = CP_2 - SP_2 = 8000 - 7200 = 800 \]

### Step 7: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP_2}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{800}{8000}\right) \times 100 = 10\% \]

### Final Answer
The loss percentage on the second TV set is **10%**.

---