A person sells two machines at Rs .396 each.On one he gains 10% and on the other he loses 10%.His profit or loss in the whole transaction is:

Options

A. No gain no loss
B. 1% loss
C. 1% profit
D. 8% profit

Answer

To solve the problem step by step, we will first calculate the cost price of each machine and then determine the overall profit or loss from the transactions.

### Step 1: Determine the Selling Price of Each Machine
The selling price of both machines is given as Rs. 396 each.

### Step 2: Calculate the Cost Price of the First Machine
For the first machine, we know that there is a gain of 10%.

Using the formula for gain percentage:
\[ \text{Gain \%} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100 \]

Let the cost price of the first machine be \( x \).
\[ 10 = \frac{396 - x}{x} \times 100 \]

Rearranging the equation:
\[ 10x = 39600 - 100x \]
\[ 10x + 100x = 39600 \]
\[ 110x = 39600 \]
\[ x = \frac{39600}{110} = 360 \]

So, the cost price of the first machine is Rs. 360.

### Step 3: Calculate the Cost Price of the Second Machine
For the second machine, there is a loss of 10%.

Using the formula for loss percentage:
\[ \text{Loss \%} = \frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100 \]

Let the cost price of the second machine be \( y \).
\[ 10 = \frac{y - 396}{y} \times 100 \]

Rearranging the equation:
\[ 10y = 100y - 39600 \]
\[ 10y + 39600 = 100y \]
\[ 39600 = 90y \]
\[ y = \frac{39600}{90} = 440 \]

So, the cost price of the second machine is Rs. 440.

### Step 4: Calculate the Total Cost Price and Total Selling Price
Total cost price of both machines:
\[ \text{Total Cost Price} = 360 + 440 = 800 \]

Total selling price of both machines:
\[ \text{Total Selling Price} = 396 + 396 = 792 \]

### Step 5: Determine Overall Profit or Loss
Now, we can calculate the overall profit or loss:
\[ \text{Loss} = \text{Total Cost Price} - \text{Total Selling Price} = 800 - 792 = 8 \]

### Step 6: Calculate the Loss Percentage
To find the loss percentage:
\[ \text{Loss \%} = \frac{\text{Loss}}{\text{Total Cost Price}} \times 100 \]
\[ \text{Loss \%} = \frac{8}{800} \times 100 = 1 \]

### Conclusion
The overall transaction results in a loss of 1%.