A man purchased a cow for Rs. 300 and sold it the same day for Rs. 360, allowing the buyer at the credit of 2 years. If the rate of interest be `7 1/7%` per annum, then the man has a gain of-

Options

A. `4 1/2 %`
B. `5 3/7 %`
C. `6%`
D. `5%`

Answer

To solve the problem step by step, we will first determine the present worth (PW) of the selling price (SP) of the cow, then calculate the gain based on the purchase price (CP).

### Step 1: Identify the given values
- Cost Price (CP) = Rs. 300
- Selling Price (SP) = Rs. 360
- Time (T) = 2 years
- Rate of Interest (R) = 7 1/7% = 7.14% = 50/7%

### Step 2: Calculate the Present Worth (PW) of the Selling Price
The formula for Present Worth (PW) is given by:
\[ PW = \frac{100 \times SP}{100 + (R \times T)} \]

Substituting the values:
\[ PW = \frac{100 \times 360}{100 + \left(\frac{50}{7} \times 2\right)} \]

### Step 3: Calculate the denominator
First, calculate \( R \times T \):
\[ R \times T = \frac{50}{7} \times 2 = \frac{100}{7} \]

Now, add this to 100:
\[ 100 + \frac{100}{7} = \frac{700 + 100}{7} = \frac{800}{7} \]

### Step 4: Substitute back into the PW formula
Now we can substitute back into the PW formula:
\[ PW = \frac{100 \times 360}{\frac{800}{7}} = \frac{36000 \times 7}{800} = \frac{252000}{800} = 315 \]

### Step 5: Calculate the Gain
Now we find the gain by subtracting the Cost Price (CP) from the Present Worth (PW):
\[ \text{Gain} = PW - CP = 315 - 300 = 15 \]

### Step 6: Calculate the Gain Percentage
To find the gain percentage, use the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{15}{300}\right) \times 100 = 5\% \]

### Final Answer
The man has a gain of **5%**.

---