The market price of article is 28% higher than its cost price. Find the profit or loss percentage if the shopkeeper gives 25% discount.

Options

A. Loss : 5%
B. Profit: 5%
C. Loss: 4%
D. Profit : 4 %

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)
Let the cost price (CP) of the article be \(100\) (this is a convenient choice for calculation).

### Step 2: Calculate the Market Price (MP)
The market price is given to be 28% higher than the cost price. Therefore, we can calculate the market price as follows:
\[ \text{Market Price (MP)} = \text{Cost Price (CP)} + 28\% \text{ of CP} \]
\[ \text{MP} = 100 + 0.28 \times 100 = 100 + 28 = 128 \]
So, the market price is \(128\).

### Step 3: Calculate the Selling Price (SP) after Discount
The shopkeeper gives a discount of 25% on the market price. We can calculate the selling price as follows:
\[ \text{Discount} = 25\% \text{ of MP} = 0.25 \times 128 = 32 \]
Now, we subtract the discount from the market price to find the selling price:
\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount} = 128 - 32 = 96 \]

### Step 4: Calculate the Loss
Now, we find the loss incurred by the shopkeeper:
\[ \text{Loss} = \text{Cost Price (CP)} - \text{Selling Price (SP)} = 100 - 96 = 4 \]

### Step 5: Calculate the Loss Percentage
Finally, we calculate the loss percentage using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{4}{100} \right) \times 100 = 4\% \]

Thus, the loss percentage is \(4\%\).

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