In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit per cent of

Options

A. `30%`
B. `32%`
C. `33%`
D. `35%`

Answer

To solve the problem step by step, we will use the given percentages of discount and profit to find the profit percentage if the article were sold at the marked price.

### Step 1: Understand the given information
- Discount (D) = 10%
- Profit (P) = 17%

### Step 2: Establish the relationship between Cost Price (CP), Marked Price (MP), and Selling Price (SP)
- When a discount is given, the Selling Price (SP) can be calculated as:
\[ SP = MP - (D \% \text{ of } MP) = MP \times \left(1 - \frac{D}{100}\right) \]
- Given that the trader makes a profit of 17% on the Cost Price (CP), we can express this as:
\[ SP = CP + (P \% \text{ of } CP) = CP \times \left(1 + \frac{P}{100}\right) \]

### Step 3: Set up the equations
From the above relationships, we can equate the two expressions for SP:
\[ MP \times \left(1 - \frac{10}{100}\right) = CP \times \left(1 + \frac{17}{100}\right) \]
This simplifies to:
\[ MP \times 0.9 = CP \times 1.17 \]

### Step 4: Rearranging the equation
We can rearrange this equation to find the ratio of CP to MP:
\[ \frac{CP}{MP} = \frac{0.9}{1.17} \]

### Step 5: Simplifying the ratio
To simplify \(\frac{0.9}{1.17}\):
- Multiply both the numerator and denominator by 100 to eliminate the decimal:
\[ \frac{90}{117} \]
- Now, we can simplify this fraction:
\[ \frac{90 \div 9}{117 \div 9} = \frac{10}{13} \]
Thus, the ratio of CP to MP is \(10:13\).

### Step 6: Calculate the profit percentage at the marked price
If the article is sold at the marked price (MP), we need to find the profit percentage:
- The Selling Price at marked price is \(MP\).
- We know from the ratio that \(CP = 10x\) and \(MP = 13x\) for some value \(x\).
- The profit when sold at marked price is:
\[ \text{Profit} = MP - CP = 13x - 10x = 3x \]
- The profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{3x}{10x}\right) \times 100 = 30\% \]

### Final Answer
If the trader sold the article at the marked price, he would have earned a profit percentage of **30%**.

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