A man purchased a cow for Rs 3000 and sold it the same day for Rs 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of

Options

A. 0.05
B. 0
C. 0.2
D. 0.1

Answer

To find the gain of the man who purchased a cow for Rs 3000 and sold it for Rs 3600 with a credit period of 2 years at an interest rate of 10% per annum, we need to calculate the present value of the selling price (Rs 3600) at the given interest rate and compare it with the cost price (Rs 3000).

### Step-by-Step Solution:

1. **Identify the Selling Price and Cost Price:**
- Cost Price (CP) = Rs 3000
- Selling Price (SP) = Rs 3600

2. **Determine the Time Period and Interest Rate:**
- Time (T) = 2 years
- Rate of Interest (R) = 10% per annum

3. **Calculate the Present Value (PV) of the Selling Price:**
The formula for Present Value is:
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \( FV \) = Future Value (Selling Price) = Rs 3600
- \( r \) = Rate of interest per annum = 10% = 0.10
- \( n \) = Number of years = 2

Plugging in the values:
\[ PV = \frac{3600}{(1 + 0.10)^2} = \frac{3600}{(1.10)^2} = \frac{3600}{1.21} \approx 2975.21 \]

4. **Calculate the Gain:**
Gain can be calculated as:
\[ Gain = SP - CP \]
However, since we are comparing the present value of the selling price with the cost price:
\[ Gain = PV - CP = 2975.21 - 3000 \approx -24.79 \]

5. **Determine the Gain Percentage:**
Since the gain is negative, we can also express it as a loss:
\[ Loss = CP - PV = 3000 - 2975.21 \approx 24.79 \]
To express this as a percentage of the cost price:
\[ Gain\% = \left(\frac{Gain}{CP}\right) \times 100 = \left(\frac{-24.79}{3000}\right) \times 100 \approx -0.826\% \]

### Final Answer:
The man has a loss of approximately Rs 24.79, which indicates that he did not gain from this transaction.