I get profit of 10% on selling a horse for Rs.3100 and a buffalo for Rs 1300 . I incur loss of 10% if I sell horse for Rs 3150 and a buffalo at its C.P. Find the difference C.P. of horse and buffalo.

Options

A. 500
B. 750
C. 3100
D. 2100

Answer

To solve the problem step by step, we need to find the cost prices (C.P.) of the horse and the buffalo and then calculate the difference between them.

### Step 1: Find the C.P. of the Horse
We know that selling the horse for Rs. 3100 gives a profit of 10%.

Let the C.P. of the horse be \( C_H \).

Using the profit formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (C.P.)} + \text{Profit} \]
\[ SP = C_H + 0.1 \times C_H = 1.1 \times C_H \]
Setting the SP to Rs. 3100:
\[ 3100 = 1.1 \times C_H \]
Now, solve for \( C_H \):
\[ C_H = \frac{3100}{1.1} = 2818.18 \text{ (approximately)} \]

### Step 2: Find the C.P. of the Buffalo
We know that selling the buffalo for Rs. 1300 also gives a profit of 10%.

Let the C.P. of the buffalo be \( C_B \).

Using the same profit formula:
\[ SP = C_B + 0.1 \times C_B = 1.1 \times C_B \]
Setting the SP to Rs. 1300:
\[ 1300 = 1.1 \times C_B \]
Now, solve for \( C_B \):
\[ C_B = \frac{1300}{1.1} = 1181.82 \text{ (approximately)} \]

### Step 3: Calculate the Loss Scenario for the Horse
Next, we consider the scenario where the horse is sold for Rs. 3150 and incurs a loss of 10%.

Using the loss formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (C.P.)} - \text{Loss} \]
\[ SP = C_H - 0.1 \times C_H = 0.9 \times C_H \]
Setting the SP to Rs. 3150:
\[ 3150 = 0.9 \times C_H \]
Now, solve for \( C_H \):
\[ C_H = \frac{3150}{0.9} = 3500 \]

### Step 4: Find C.P. of the Buffalo in the Loss Scenario
We know that the buffalo is sold at its C.P. with a loss of 10%.

Using the loss formula:
\[ SP = C_B - 0.1 \times C_B = 0.9 \times C_B \]
Since the buffalo is sold at its C.P., we can set \( SP = C_B \):
\[ C_B = 0.9 \times C_B \]
This means the C.P. of the buffalo remains the same as calculated earlier, which is Rs. 1181.82.

### Step 5: Calculate the Difference in C.P.
Now, we need to find the difference between the C.P. of the horse and the C.P. of the buffalo:
\[ \text{Difference} = C_H - C_B = 3500 - 1181.82 = 2318.18 \]

### Final Answer
The difference in the cost prices of the horse and the buffalo is approximately Rs. 2318.18.