A trader gives a discount of 30% on the marked price. To earn profit of 5%, by how much percent should he mark the price of his goods higher than its cost price?

Options

A. 40
B. 35
C. 50
D. 25

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define the Cost Price (CP)
Let the Cost Price (CP) be denoted as \( X \).

### Step 2: Calculate the Selling Price (SP) for a 5% Profit
To earn a profit of 5%, the Selling Price (SP) can be calculated as:
\[ SP = CP + \text{Profit} = X + 0.05X = 1.05X \]

### Step 3: Define the Marked Price (MP)
Let the Marked Price (MP) be denoted as \( Y \).

### Step 4: Calculate the Discount on the Marked Price
The trader gives a discount of 30% on the Marked Price. Therefore, the discount amount is:
\[ \text{Discount} = 30\% \text{ of } Y = 0.3Y \]

### Step 5: Calculate the Selling Price (SP) after Discount
The Selling Price after applying the discount is:
\[ SP = MP - \text{Discount} = Y - 0.3Y = 0.7Y \]

### Step 6: Set the Selling Prices Equal
Since both expressions represent the Selling Price, we can set them equal to each other:
\[ 1.05X = 0.7Y \]

### Step 7: Solve for the Marked Price in terms of Cost Price
Rearranging the equation to find \( Y \):
\[ Y = \frac{1.05X}{0.7} = 1.5X \]

### Step 8: Calculate the Percentage Increase from Cost Price to Marked Price
Now, we need to find out by how much percent the Marked Price is higher than the Cost Price:
\[ \text{Percentage Increase} = \frac{Y - X}{X} \times 100 \]
Substituting \( Y = 1.5X \):
\[ \text{Percentage Increase} = \frac{1.5X - X}{X} \times 100 = \frac{0.5X}{X} \times 100 = 50\% \]

### Conclusion
The trader should mark the price of his goods 50% higher than its Cost Price.