A trader marks his goods at 20% above the cost price. If he allows a discount of 5% for cash down payment, his profit percent for such a transaction is

Options

A. `15%`
B. `12%`
C. `14%`
D. `17%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)
Let the Cost Price (CP) of the goods be \( x \).

### Step 2: Calculate the Marked Price (MP)
The trader marks his goods at 20% above the cost price. Therefore, the Marked Price (MP) can be calculated as:
\[ MP = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

### Step 3: Calculate the Selling Price (SP) after Discount
The trader allows a discount of 5% on the marked price. Thus, the Selling Price (SP) after the discount is:
\[ SP = MP - 5\% \text{ of } MP = MP - 0.05 \times MP = MP \times (1 - 0.05) = MP \times 0.95 \]
Substituting the value of MP:
\[ SP = 1.2x \times 0.95 = 1.14x \]

### Step 4: Calculate the Profit
Profit is calculated as the difference between the Selling Price and the Cost Price:
\[ \text{Profit} = SP - CP = 1.14x - x = 0.14x \]

### Step 5: Calculate the Profit Percentage
Profit Percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{0.14x}{x} \right) \times 100 = 0.14 \times 100 = 14\% \]

### Conclusion
The profit percentage for such a transaction is **14%**.

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