On selling an article for Rs. 255. a shopkeeper loses 15%. At how much (in Rs.) he should sell the article in order to earn a profit of 20%?

Options

A. A) 280
B. B) 160
C. C) 200
D. D) 360

Answer

To solve the problem step by step, we will first find the cost price of the article and then determine the selling price required to achieve a profit of 20%.

### Step 1: Determine the Cost Price (CP)
We know that the shopkeeper sold the article for Rs. 255 and incurred a loss of 15%.

Let the Cost Price (CP) be represented as \( x \).

Since there is a loss of 15%, the Selling Price (SP) can be calculated as:
\[ SP = CP - (15\% \text{ of } CP) = CP - 0.15 \times CP = 0.85 \times CP \]
Given that the Selling Price (SP) is Rs. 255, we can set up the equation:
\[ 0.85x = 255 \]

### Step 2: Solve for Cost Price (CP)
To find \( x \), we rearrange the equation:
\[ x = \frac{255}{0.85} \]
Calculating this gives:
\[ x = 300 \]
So, the Cost Price (CP) of the article is Rs. 300.

### Step 3: Calculate the Selling Price for a 20% Profit
To find the Selling Price (SP) that would yield a profit of 20%, we can use the formula:
\[ SP = CP + (20\% \text{ of } CP) = CP + 0.20 \times CP = 1.20 \times CP \]
Substituting the Cost Price we found:
\[ SP = 1.20 \times 300 \]
Calculating this gives:
\[ SP = 360 \]

### Conclusion
The selling price at which the shopkeeper should sell the article to earn a profit of 20% is Rs. 360.

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