A person sell two horses for rupees 480 each. On the first horse he gains 25 percent and on the second horse he losses 25 percent. Find the percent gain or loss in the transaction

Options

A. loss 6.75%
B. gain 6.75%
C. loss 6.25%
D. gain 6.25%

Explanation

To solve the problem, we need to find out the cost price of each horse and then determine the overall gain or loss from the transaction.

### Step 1: Calculate the Cost Price of the First Horse
Let the cost price of the first horse be \( CP_1 \).

Given that the selling price (SP) of the first horse is Rs. 480 and the gain is 25%, we can use the formula for selling price:

\[ SP = CP + \text{Gain} \]

Where Gain is calculated as:

\[ \text{Gain} = \frac{25}{100} \times CP_1 = 0.25 \times CP_1 \]

Substituting into the selling price formula:

\[ 480 = CP_1 + 0.25 \times CP_1 \]

This simplifies to:

\[ 480 = 1.25 \times CP_1 \]

Now, solving for \( CP_1 \):

\[ CP_1 = \frac{480}{1.25} = 384 \]

### Step 2: Calculate the Cost Price of the Second Horse
Let the cost price of the second horse be \( CP_2 \).

Given that the selling price (SP) of the second horse is also Rs. 480 and the loss is 25%, we can use the formula for selling price:

\[ SP = CP - \text{Loss} \]

Where Loss is calculated as:

\[ \text{Loss} = \frac{25}{100} \times CP_2 = 0.25 \times CP_2 \]

Substituting into the selling price formula:

\[ 480 = CP_2 - 0.25 \times CP_2 \]

This simplifies to:

\[ 480 = 0.75 \times CP_2 \]

Now, solving for \( CP_2 \):

\[ CP_2 = \frac{480}{0.75} = 640 \]

### Step 3: Calculate the Total Cost Price and Total Selling Price
Now, we can find the total cost price and total selling price of both horses.

- Total Cost Price (TCP) = \( CP_1 + CP_2 = 384 + 640 = 1024 \)
- Total Selling Price (TSP) = \( 480 + 480 = 960 \)

### Step 4: Calculate the Overall Gain or Loss
To find the overall gain or loss, we subtract the total cost price from the total selling price:

\[ \text{Gain or Loss} = TSP - TCP = 960 - 1024 = -64 \]

Since the result is negative, it indicates a loss.

### Step 5: Calculate the Percentage Loss
To find the percentage loss, we use the formula:

\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Total Cost Price}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage Loss} = \left( \frac{64}{1024} \right) \times 100 = 6.25\% \]

### Final Answer
The person incurs a loss of **6.25%** in the transaction.

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