By selling an article at `2/3` of the marked price, there is a loss of 10%. The profit percent, when the article is sold at the marked price, is

Options

A. 0.2
B. 0.3
C. 0.35
D. 0.4

Answer

To solve the problem step by step, we will use the concepts of cost price (CP), marked price (MP), and selling price (SP).

### Step 1: Define the Variables
Let:
- CP = Cost Price
- MP = Marked Price
- SP = Selling Price

### Step 2: Understand the Given Information
According to the problem:
- The article is sold at \( \frac{2}{3} \) of the marked price.
- There is a loss of 10% when sold at this price.

### Step 3: Express Selling Price in Terms of Marked Price
From the information given, we can express the selling price (SP) as:
\[ SP = \frac{2}{3} \times MP \]

### Step 4: Relate Selling Price to Cost Price
Since there is a loss of 10%, we can express this relationship as:
\[ SP = CP - 0.1 \times CP \]
This simplifies to:
\[ SP = 0.9 \times CP \]

### Step 5: Set the Two Expressions for Selling Price Equal
Now, we can set the two expressions for SP equal to each other:
\[ \frac{2}{3} \times MP = 0.9 \times CP \]

### Step 6: Rearrange to Find the Relationship Between MP and CP
Rearranging the equation gives us:
\[ MP = \frac{0.9 \times CP \times 3}{2} \]
\[ MP = 1.35 \times CP \]

### Step 7: Calculate Profit Percentage When Sold at Marked Price
When the article is sold at the marked price (MP), the selling price is equal to MP. The profit can be calculated as:
\[ \text{Profit} = MP - CP \]
Substituting the expression for MP:
\[ \text{Profit} = 1.35 \times CP - CP \]
\[ \text{Profit} = 0.35 \times CP \]

### Step 8: Calculate the Profit Percentage
The profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the profit we found:
\[ \text{Profit Percentage} = \left( \frac{0.35 \times CP}{CP} \right) \times 100 \]
\[ \text{Profit Percentage} = 0.35 \times 100 = 35\% \]

### Final Answer
The profit percentage when the article is sold at the marked price is **35%**.

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