A man sells two cows, one at the profit of 5 % and one at the loss of 5 %, his profit or loss percentage is

Options

A. `1/3%`
B. `1/4%`
C. `1/5%`
D. `2/3%`

Answer

To solve the problem of finding the overall profit or loss percentage when a man sells two cows, one at a profit of 5% and the other at a loss of 5%, we can follow these steps:

### Step 1: Understand the Selling Prices
Let’s assume the cost price of the first cow is \( CP_1 \) and the cost price of the second cow is \( CP_2 \).

### Step 2: Calculate Selling Prices
1. **Selling Price of the first cow (SP1)**:
\[ SP_1 = CP_1 + (5\% \text{ of } CP_1) = CP_1 + 0.05 \times CP_1 = 1.05 \times CP_1 \]

2. **Selling Price of the second cow (SP2)**:
\[ SP_2 = CP_2 - (5\% \text{ of } CP_2) = CP_2 - 0.05 \times CP_2 = 0.95 \times CP_2 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
- **Total Cost Price (CP)**:
\[ CP = CP_1 + CP_2 \]

- **Total Selling Price (SP)**:
\[ SP = SP_1 + SP_2 = (1.05 \times CP_1) + (0.95 \times CP_2) \]

### Step 4: Calculate Overall Profit or Loss
To find the overall profit or loss, we need to compare the total selling price with the total cost price.

### Step 5: Use the Formula for Profit or Loss Percentage
The profit or loss percentage can be calculated using the formula:
\[ \text{Profit or Loss Percentage} = \frac{SP - CP}{CP} \times 100 \]

### Step 6: Substitute the Values
From the previous steps, we know:
\[ SP = 1.05 \times CP_1 + 0.95 \times CP_2 \]
\[ CP = CP_1 + CP_2 \]

Now, let’s calculate the loss:
- The loss can be calculated as:
\[ \text{Loss} = CP - SP \]

### Step 7: Calculate the Loss Percentage
Since we know that when there is a 5% profit and a 5% loss, the overall result is a loss:
\[ \text{Loss Percentage} = \frac{(5 \times 5)}{100} = \frac{25}{100} = 0.25 \text{ or } 1/4 \text{ percent} \]

### Conclusion
Thus, the overall loss percentage when selling one cow at a profit of 5% and another at a loss of 5% is **1/4 percent**.

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