A farmer sell his two cows. One one, he gains 25% and on the other, he losses 25%. Find his gain or loss per cent in the whole transaction.

Options

A. 6.25% profit
B. 6.25% loss
C. neither profit nor loss
D. none of the above

Answer

To solve the problem of the farmer selling two cows, one with a gain of 25% and the other with a loss of 25%, we will use the following steps:

### Step 1: Understand the Problem
The farmer sells two cows:
- For the first cow, he gains 25%.
- For the second cow, he loses 25%.

We need to find the overall gain or loss percentage from these transactions.

### Step 2: Assume the Cost Prices
Let's assume the cost price of the first cow is \( CP_1 = 100 \) (this is an arbitrary choice to simplify calculations).
Then, the selling price (SP) of the first cow, with a gain of 25%, can be calculated as follows:
\[ SP_1 = CP_1 + (25\% \text{ of } CP_1) = 100 + (0.25 \times 100) = 100 + 25 = 125 \]

### Step 3: Calculate the Selling Price of the Second Cow
Now, for the second cow, we assume the cost price is \( CP_2 = 100 \) as well.
The selling price (SP) of the second cow, with a loss of 25%, can be calculated as follows:
\[ SP_2 = CP_2 - (25\% \text{ of } CP_2) = 100 - (0.25 \times 100) = 100 - 25 = 75 \]

### Step 4: Calculate Total Cost Price and Total Selling Price
Now, we can calculate the total cost price and total selling price of both cows:
\[ \text{Total Cost Price} = CP_1 + CP_2 = 100 + 100 = 200 \]
\[ \text{Total Selling Price} = SP_1 + SP_2 = 125 + 75 = 200 \]

### Step 5: Determine Overall Gain or Loss
Now, we can find out if there is an overall gain or loss:
\[ \text{Total Gain or Loss} = \text{Total Selling Price} - \text{Total Cost Price} = 200 - 200 = 0 \]

### Step 6: Calculate Gain or Loss Percentage
Since there is no gain or loss, the percentage is:
\[ \text{Gain or Loss Percentage} = \left( \frac{\text{Total Gain or Loss}}{\text{Total Cost Price}} \right) \times 100 = \left( \frac{0}{200} \right) \times 100 = 0\% \]

### Conclusion
The farmer neither gains nor loses in the whole transaction.