A man sells two tables at the same price. On one he makes a profit of 10% and on the other he suffers a loss of 10%. His loss per cent on the whole transaction is :

Options

A. 0
B. 1
C. 2
D. 5

Answer

To solve the problem step by step, we will analyze the transactions involving the two tables sold by the man.

### Step 1: Define Variables
Let the selling price (SP) of each table be \( S \). Since both tables are sold at the same price, we can denote the cost price (CP) of the first table as \( CP_1 \) and the cost price of the second table as \( CP_2 \).

### Step 2: Calculate Cost Price of the First Table
For the first table, the man makes a profit of 10%. We can express this as:
\[ SP = CP_1 + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = 10\% \text{ of } CP_1 = \frac{10}{100} \times CP_1 = 0.1 \times CP_1 \]
Thus,
\[ S = CP_1 + 0.1 \times CP_1 = 1.1 \times CP_1 \]
From this, we can derive:
\[ CP_1 = \frac{S}{1.1} \]

### Step 3: Calculate Cost Price of the Second Table
For the second table, the man suffers a loss of 10%. The loss can be expressed as:
\[ SP = CP_2 - \text{Loss} \]
The loss is:
\[ \text{Loss} = 10\% \text{ of } CP_2 = \frac{10}{100} \times CP_2 = 0.1 \times CP_2 \]
Thus,
\[ S = CP_2 - 0.1 \times CP_2 = 0.9 \times CP_2 \]
From this, we can derive:
\[ CP_2 = \frac{S}{0.9} \]

### Step 4: Calculate Total Cost Price
Now, we can calculate the total cost price of both tables:
\[ \text{Total CP} = CP_1 + CP_2 = \frac{S}{1.1} + \frac{S}{0.9} \]
To add these fractions, we need a common denominator, which is \( 0.99 \):
\[ \text{Total CP} = \frac{S \cdot 0.9}{0.99} + \frac{S \cdot 1.1}{0.99} = \frac{0.9S + 1.1S}{0.99} = \frac{2S}{0.99} \]

### Step 5: Calculate Total Selling Price
The total selling price for both tables is:
\[ \text{Total SP} = S + S = 2S \]

### Step 6: Calculate Net Loss
Now, we can find the net loss:
\[ \text{Net Loss} = \text{Total CP} - \text{Total SP} = \frac{2S}{0.99} - 2S \]
To simplify:
\[ \text{Net Loss} = 2S \left( \frac{1}{0.99} - 1 \right) = 2S \left( \frac{1 - 0.99}{0.99} \right) = 2S \left( \frac{0.01}{0.99} \right) = \frac{0.02S}{0.99} \]

### Step 7: Calculate Loss Percentage
Finally, we calculate the loss percentage:
\[ \text{Loss Percentage} = \left( \frac{\text{Net Loss}}{\text{Total SP}} \right) \times 100 = \left( \frac{\frac{0.02S}{0.99}}{2S} \right) \times 100 \]
This simplifies to:
\[ \text{Loss Percentage} = \left( \frac{0.02}{1.98} \right) \times 100 \approx 1.01\% \]

### Conclusion
Thus, the man suffers a loss of approximately **1%** on the whole transaction.