A man gains 10% by selling an article for a certain price.If he sells it at double the price,then the profit made is

Options

A. `120%`
B. `20%`
C. `405`
D. `100%`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Given Information
We know that a man gains 10% profit by selling an article at a certain price. We need to find out the profit percentage if he sells it at double that price.

**Hint:** Identify the initial selling price and how it relates to the cost price.

### Step 2: Define the Cost Price (CP)
Let the cost price (CP) of the article be \( CP \).

**Hint:** Assign a variable to the cost price for easier calculations.

### Step 3: Calculate the Selling Price (SP) with 10% Profit
Since the man gains 10% profit, the selling price (SP) can be calculated as:
\[ SP_{\text{old}} = CP + \left( \frac{10}{100} \times CP \right) = CP \times \left( 1 + \frac{10}{100} \right) = CP \times \frac{110}{100} = \frac{11}{10} \times CP \]

**Hint:** Use the formula for selling price based on profit percentage.

### Step 4: Calculate the New Selling Price (SP)
If he sells the article at double the old selling price, then:
\[ SP_{\text{new}} = 2 \times SP_{\text{old}} = 2 \times \left( \frac{11}{10} \times CP \right) = \frac{22}{10} \times CP = 2.2 \times CP \]

**Hint:** Remember that doubling the selling price means multiplying by 2.

### Step 5: Calculate the Profit (P)
The profit can be calculated as:
\[ P = SP_{\text{new}} - CP = (2.2 \times CP) - CP = 1.2 \times CP \]

**Hint:** Profit is the difference between the new selling price and the cost price.

### Step 6: Calculate the Profit Percentage
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{1.2 \times CP}{CP} \right) \times 100 = 1.2 \times 100 = 120\% \]

**Hint:** Use the profit and cost price to find the percentage increase.

### Final Answer
The profit percentage when the article is sold at double the price is **120%**.

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