A trader gives a discount of `20%` on the marked price. To earn profit of `12%` , by how much percent should he mark the price of his goods higher than its cost price?

Options

A. 20
B. 40
C. 25
D. 35

Answer

To solve the problem, we need to find out by what percentage the marked price (MP) should be higher than the cost price (CP) to achieve a desired profit after giving a discount.

### Step-by-step Solution:

1. **Understand the Given Information:**
- Discount = 20%
- Profit = 12%

2. **Express the Selling Price (SP) in terms of Marked Price (MP):**
- If the marked price is MP, after a 20% discount, the selling price (SP) can be calculated as:
\[ SP = MP \times (1 - \text{Discount}) \]
\[ SP = MP \times (1 - 0.20) = MP \times 0.80 \]

3. **Express the Selling Price (SP) in terms of Cost Price (CP):**
- To earn a profit of 12%, the selling price can also be expressed as:
\[ SP = CP \times (1 + \text{Profit}) \]
\[ SP = CP \times (1 + 0.12) = CP \times 1.12 \]

4. **Set the Two Expressions for Selling Price Equal:**
- Since both expressions represent the selling price, we can set them equal to each other:
\[ MP \times 0.80 = CP \times 1.12 \]

5. **Rearranging the Equation:**
- To find the relationship between MP and CP, we can rearrange the equation:
\[ MP = \frac{CP \times 1.12}{0.80} \]

6. **Calculating the Ratio of MP to CP:**
- Simplifying the right side:
\[ MP = CP \times \frac{1.12}{0.80} = CP \times 1.4 \]

7. **Finding the Percentage Increase:**
- The marked price is 1.4 times the cost price, which means:
\[ MP = CP + 0.4 \times CP \]
- Therefore, the percentage increase in the marked price over the cost price is:
\[ \text{Percentage Increase} = \left(\frac{MP - CP}{CP}\right) \times 100 = \left(\frac{0.4 \times CP}{CP}\right) \times 100 = 40\% \]

### Final Answer:
The marked price should be marked 40% higher than the cost price.

---