A man sold two cows at Rs1995 each. On one he lost 10% and on the other he gained 10%. What his gain or loss percent?

Options

A. `4%`
B. `2%`
C. `0.5%`
D. `1%`

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Selling Price
The man sold two cows at Rs 1995 each. Therefore, the selling price (SP) for each cow is:
\[ SP_1 = SP_2 = 1995 \]

### Step 2: Calculate the Cost Price of Each Cow
1. **For the first cow** (where he incurred a loss of 10%):
- Let the cost price (CP) of the first cow be \( CP_1 \).
- Since he lost 10%, the selling price can be expressed as:
\[ SP_1 = CP_1 - (10\% \text{ of } CP_1) = CP_1 - 0.1 \times CP_1 = 0.9 \times CP_1 \]
- Rearranging gives:
\[ CP_1 = \frac{SP_1}{0.9} = \frac{1995}{0.9} = 2216.67 \]

2. **For the second cow** (where he gained 10%):
- Let the cost price (CP) of the second cow be \( CP_2 \).
- Since he gained 10%, the selling price can be expressed as:
\[ SP_2 = CP_2 + (10\% \text{ of } CP_2) = CP_2 + 0.1 \times CP_2 = 1.1 \times CP_2 \]
- Rearranging gives:
\[ CP_2 = \frac{SP_2}{1.1} = \frac{1995}{1.1} = 1813.64 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
- Total Cost Price (CP) of both cows:
\[ Total\ CP = CP_1 + CP_2 = 2216.67 + 1813.64 = 4030.31 \]
- Total Selling Price (SP) of both cows:
\[ Total\ SP = SP_1 + SP_2 = 1995 + 1995 = 3990 \]

### Step 4: Calculate Gain or Loss
- To find the overall gain or loss:
\[ Loss = Total\ CP - Total\ SP = 4030.31 - 3990 = 40.31 \]

### Step 5: Calculate Loss Percentage
- The loss percentage can be calculated using the formula:
\[ Loss\% = \left( \frac{Loss}{Total\ CP} \right) \times 100 = \left( \frac{40.31}{4030.31} \right) \times 100 \approx 1\% \]

### Final Answer
The man incurred a loss of approximately **1%**.

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