A shopkeeper buys an article for Rs. 180. After allowing a discount of `10%` on his marked price, he wants to earn a profit of `20%` His marked price must be

Options

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

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Cost Price (CP) = Rs. 180
- Profit Percentage = 20%
- Discount Percentage = 10%

2. **Let the Marked Price (MP) be X:**
- We denote the marked price of the article as X.

3. **Calculate the Selling Price (SP) after Discount:**
- The discount on the marked price is 10% of X.
- Therefore, the selling price after discount can be calculated as:
\[ SP = MP - \text{Discount} = X - 0.10X = 0.90X \]

4. **Set Up the Profit Equation:**
- We know that Profit Percentage is given by the formula:
\[ \text{Profit Percentage} = \frac{SP - CP}{CP} \times 100 \]
- Substituting the known values into the equation:
\[ 20 = \frac{0.90X - 180}{180} \times 100 \]

5. **Simplify the Equation:**
- Divide both sides by 100:
\[ 0.20 = \frac{0.90X - 180}{180} \]
- Multiply both sides by 180:
\[ 36 = 0.90X - 180 \]

6. **Rearranging the Equation:**
- Add 180 to both sides:
\[ 0.90X = 216 \]

7. **Solve for X (Marked Price):**
- Divide both sides by 0.90:
\[ X = \frac{216}{0.90} = 240 \]

8. **Conclusion:**
- The marked price (MP) must be Rs. 240.

### Final Answer:
The marked price must be **Rs. 240**.

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