A shopkeeper buys an article for Rs. 180. He wishes to gain 20% after allowing a discount of 10% on the marked price to the customer. The marked price will be

Options

A. Rs. 210
B. Rs. 240
C. Rs. 270
D. Rs. 300

Answer

To find the marked price of the article, we will follow these steps:

### Step 1: Determine the Cost Price and Desired Profit
The cost price (CP) of the article is given as Rs. 180. The shopkeeper wishes to gain a profit of 20%.

**Calculation:**
Profit = 20% of CP = 20/100 × 180 = Rs. 36

### Step 2: Calculate the Selling Price
The selling price (SP) can be calculated by adding the profit to the cost price.

**Calculation:**
SP = CP + Profit = 180 + 36 = Rs. 216

### Step 3: Understand the Relationship Between Marked Price and Selling Price
The shopkeeper allows a discount of 10% on the marked price (MP) to arrive at the selling price. This means that the selling price is 90% of the marked price.

**Equation:**
SP = MP - Discount
Since the discount is 10% of MP, we can express it as:
SP = MP × (1 - 10/100) = MP × 0.90

### Step 4: Set Up the Equation
We know the selling price (SP) is Rs. 216. Therefore, we can set up the equation as follows:

216 = MP × 0.90

### Step 5: Solve for Marked Price
To find the marked price (MP), we can rearrange the equation:

MP = 216 / 0.90

**Calculation:**
MP = 240

### Conclusion
The marked price of the article is Rs. 240.

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