A trader sells two cycles at Rs. 1188 each and gains 10`%` on the first and loses 10`%` on the second. What is the profit or loss per cent on the whole?

Options

A. `1%` loss
B. `1%` gain
C. `2%` loss
D. No loss no gain

Answer

To find the overall profit or loss percentage when a trader sells two cycles at Rs. 1188 each, gaining 10% on the first cycle and losing 10% on the second cycle, we can follow these steps:

### Step 1: Calculate the Cost Price (CP) of the First Cycle
Let the Cost Price of the first cycle be \( CP_1 \).
Given that the selling price (SP) is Rs. 1188 and the gain is 10%, we can use the formula for selling price:
\[ SP = CP + \text{Gain} \]
The gain can be expressed as:
\[ \text{Gain} = \frac{10}{100} \times CP_1 = 0.1 \times CP_1 \]
Thus, we can write:
\[ 1188 = CP_1 + 0.1 \times CP_1 \]
\[ 1188 = 1.1 \times CP_1 \]
Now, solving for \( CP_1 \):
\[ CP_1 = \frac{1188}{1.1} = 1080 \]

### Step 2: Calculate the Cost Price (CP) of the Second Cycle
Let the Cost Price of the second cycle be \( CP_2 \).
Given that the selling price (SP) is Rs. 1188 and the loss is 10%, we can express the loss as:
\[ \text{Loss} = \frac{10}{100} \times CP_2 = 0.1 \times CP_2 \]
Thus, we can write:
\[ 1188 = CP_2 - 0.1 \times CP_2 \]
\[ 1188 = 0.9 \times CP_2 \]
Now, solving for \( CP_2 \):
\[ CP_2 = \frac{1188}{0.9} = 1320 \]

### Step 3: Calculate Total Cost Price (CP) and Total Selling Price (SP)
Now, we can find the total cost price and total selling price:
\[ \text{Total CP} = CP_1 + CP_2 = 1080 + 1320 = 2400 \]
\[ \text{Total SP} = 1188 + 1188 = 2376 \]

### Step 4: Calculate Overall Profit or Loss
Now, we can find the overall profit or loss:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 2400 - 2376 = 24 \]

### Step 5: Calculate Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{24}{2400} \right) \times 100 = 1\% \]

### Conclusion
The overall result is a loss of 1%.