After selling an article in Rs 1060 a shopkeeper gains 20% more profit as he lost by selling it in Rs 950. What will be the SP of article if he wants to earn 32% profit?

Options

A. Rs 1000
B. Rs 1210
C. Rs 1300
D. Rs 1320

Answer

To solve the problem step-by-step, let's break it down:

### Step 1: Understand the given information
The shopkeeper sells an article for Rs. 1060 and gains 20% more profit than the loss he incurred when he sold it for Rs. 950.

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

### Step 3: Calculate the loss when sold for Rs. 950
When the article is sold for Rs. 950, the shopkeeper incurs a loss. The loss can be expressed as:
\[ \text{Loss} = \text{CP} - \text{Selling Price} = x - 950 \]
The loss percentage can be calculated as:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{CP}} \times 100 = \frac{x - 950}{x} \times 100 \]

### Step 4: Calculate the profit when sold for Rs. 1060
When the article is sold for Rs. 1060, the profit can be expressed as:
\[ \text{Profit} = \text{Selling Price} - \text{CP} = 1060 - x \]
The profit percentage can be calculated as:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{CP}} \times 100 = \frac{1060 - x}{x} \times 100 \]

### Step 5: Set up the equation based on the problem statement
According to the problem, the profit when selling at Rs. 1060 is 20% more than the loss when selling at Rs. 950. This can be expressed as:
\[ 1060 - x = 1.2 \times (x - 950) \]

### Step 6: Solve the equation
Expanding the equation:
\[ 1060 - x = 1.2x - 1140 \]
Rearranging gives:
\[ 1060 + 1140 = 1.2x + x \]
\[ 2200 = 2.2x \]
Dividing both sides by 2.2:
\[ x = \frac{2200}{2.2} = 1000 \]

### Step 7: Calculate the selling price for a 32% profit
To find the selling price (SP) for a 32% profit, we use the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where Profit is calculated as:
\[ \text{Profit} = \text{CP} \times \frac{32}{100} = 1000 \times 0.32 = 320 \]
Thus, the selling price for a 32% profit is:
\[ \text{SP} = 1000 + 320 = 1320 \]

### Final Answer
The selling price of the article if he wants to earn a 32% profit is Rs. 1320.

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