Two motor cars were sold for Rs. 9,900 each, gaining 10% on one and losing 10% on the other. The gain or loss per cent in the whole transaction is :

Options

A. Neither loss no gain
B. `(1)/(99)%` gain
C. `(100)/(99)%` profit
D. `1%` loss

Answer

To solve the problem step by step, we will calculate the cost price (CP) of each car, the selling price (SP), and then determine the overall gain or loss percentage.

### Step 1: Determine the Selling Price (SP) of each car
Both cars were sold for Rs. 9,900 each.

SP of Car 1 = Rs. 9,900
SP of Car 2 = Rs. 9,900

### Step 2: Calculate the Cost Price (CP) of Car 1
Car 1 was sold at a gain of 10%.
Let the CP of Car 1 be \( CP_1 \).

Using the formula for selling price with profit:
\[ SP = CP + \text{Gain} \]
The gain can be expressed as:
\[ \text{Gain} = 10\% \text{ of } CP_1 = \frac{10}{100} \times CP_1 = 0.1 \times CP_1 \]
Thus, we can write:
\[ 9900 = CP_1 + 0.1 \times CP_1 \]
\[ 9900 = 1.1 \times CP_1 \]
Now, solving for \( CP_1 \):
\[ CP_1 = \frac{9900}{1.1} = 9000 \]

### Step 3: Calculate the Cost Price (CP) of Car 2
Car 2 was sold at a loss of 10%.
Let the CP of Car 2 be \( CP_2 \).

Using the formula for selling price with loss:
\[ SP = CP - \text{Loss} \]
The loss can be expressed as:
\[ \text{Loss} = 10\% \text{ of } CP_2 = \frac{10}{100} \times CP_2 = 0.1 \times CP_2 \]
Thus, we can write:
\[ 9900 = CP_2 - 0.1 \times CP_2 \]
\[ 9900 = 0.9 \times CP_2 \]
Now, solving for \( CP_2 \):
\[ CP_2 = \frac{9900}{0.9} = 11000 \]

### Step 4: Calculate the Total Cost Price (CP) and Selling Price (SP)
Total CP = \( CP_1 + CP_2 \)
Total CP = \( 9000 + 11000 = 20000 \)

Total SP = \( SP_1 + SP_2 \)
Total SP = \( 9900 + 9900 = 19800 \)

### Step 5: Determine the Overall Gain or Loss
Now, we can find the overall gain or loss:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 20000 - 19800 = 200 \]

### Step 6: Calculate the Loss Percentage
Using the formula for loss percentage:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{200}{20000} \right) \times 100 = 1\% \]

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