A trader marks his goods 25% above the cost price . He then sells them at a discount of 25%. If the cost price is Rs. 500, then find the loss or gain percentage.

Options

A. Loss, 5.25%
B. Gain, 5.25%
C. Gain. 7.15%
D. Loss. 6.25%

Answer

To solve the problem step by step, we will follow the given information and calculate the necessary values.

### Step 1: Identify the Cost Price (CP)
The cost price of the goods is given as:
\[ \text{Cost Price (CP)} = Rs. 500 \]

### Step 2: Calculate the Marked Price (MP)
The trader marks his goods 25% above the cost price. To find the marked price, we calculate 25% of the cost price and add it to the cost price.

\[ \text{Marked Price (MP)} = CP + (25\% \text{ of } CP) \]
\[ = 500 + \left( \frac{25}{100} \times 500 \right) \]
\[ = 500 + 125 = Rs. 625 \]

### Step 3: Calculate the Selling Price (SP)
The trader sells the goods at a discount of 25% on the marked price. To find the selling price, we calculate 25% of the marked price and subtract it from the marked price.

\[ \text{Selling Price (SP)} = MP - (25\% \text{ of } MP) \]
\[ = 625 - \left( \frac{25}{100} \times 625 \right) \]
\[ = 625 - 156.25 = Rs. 468.75 \]

### Step 4: Calculate the Loss
Now, we can determine if there is a loss or a gain by comparing the selling price with the cost price. Since the selling price is less than the cost price, there is a loss.

\[ \text{Loss} = CP - SP \]
\[ = 500 - 468.75 = Rs. 31.25 \]

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

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
\[ = \left( \frac{31.25}{500} \right) \times 100 \]
\[ = 0.0625 \times 100 = 6.25\% \]

### Final Answer
The loss percentage is **6.25%**.

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