The marked price of an article is ₹ 500. The shopkeeper allows a discount of 5% and still earns a profit of 25%. The cost price of the article is

Question

Accepted Answer

Here's a detailed explanation for the question, justifying why Option 4 is correct and why the others are incorrect:

**1. Justification for Option 4 (₹ 380) being correct:**

To find the cost price, we first need to determine the selling price of the article.

*   **Step 1: Calculate the Selling Price (SP).**
    The marked price (MP) of the article is ₹ 500.
    The shopkeeper allows a discount of 5% on the marked price.
    Discount amount = 5% of MP = 5/100 * ₹ 500 = ₹ 25.
    Selling Price (SP) = Marked Price - Discount
    SP = ₹ 500 - ₹ 25 = ₹ 475.

*   **Step 2: Calculate the Cost Price (CP).**
    The shopkeeper earns a profit of 25% on the cost price.
    We know the formula relating Selling Price, Cost Price, and Profit Percentage:
    SP = CP * (1 + Profit Percentage / 100)
    ₹ 475 = CP * (1 + 25/100)
    ₹ 475 = CP * (1 + 0.25)
    ₹ 475 = CP * 1.25
    To find CP, divide SP by 1.25:
    CP = ₹ 475 / 1.25
    CP = ₹ 380.

Therefore, the cost price of the article is ₹ 380, which matches Option 4.

**2. Explanation for why other options are incorrect:**

Let's assume the calculated Selling Price (SP) is ₹ 475, as derived above. We will check if the given profit percentage (25%) holds true for the other options if they were the Cost Price.

*   **Option 1: ₹ 280**
    If the Cost Price (CP) were ₹ 280, and the Selling Price (SP) is ₹ 475.
    Profit = SP - CP = ₹ 475 - ₹ 280 = ₹ 195.
    Profit Percentage = (Profit / CP) * 100 = (₹ 195 / ₹ 280) * 100 ≈ 69.64%.
    This is not 25%, so Option 1 is incorrect.

*   **Option 2: ₹ 225**
    If the Cost Price (CP) were ₹ 225, and the Selling Price (SP) is ₹ 475.
    Profit = SP - CP = ₹ 475 - ₹ 225 = ₹ 250.
    Profit Percentage = (Profit / CP) * 100 = (₹ 250 / ₹ 225) * 100 ≈ 111.11%.
    This is not 25%, so Option 2 is incorrect.

*   **Option 3: ₹ 425**
    If the Cost Price (CP) were ₹ 425, and the Selling Price (SP) is ₹ 475.
    Profit = SP - CP = ₹ 475 - ₹ 425 = ₹ 50.
    Profit Percentage = (Profit / CP) * 100 = (₹ 50 / ₹ 425) * 100 ≈ 11.76%.
    This is not 25%, so Option 3 is incorrect.

Based on the calculations, only a cost price of ₹ 380 results in a 25% profit when the selling price is ₹ 475.