While selling an article for Rs. 18450, a person suffered a loss of 50%. At what price he sould have sold the article (in Rs. ) to earn a profie of 50% ?

Options

A. 13837
B. 52000
C. 55350
D. 56775

Answer

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

### Step 1: Understand the given information
We know that the selling price (SP) of the article is Rs. 18450 and the loss incurred is 50%.

### Step 2: Calculate the Cost Price (CP)
The formula to calculate the cost price when there is a loss is:
\[ \text{CP} = \frac{\text{SP} \times 100}{100 - \text{Loss Percentage}} \]
Substituting the values:
\[ \text{CP} = \frac{18450 \times 100}{100 - 50} \]
\[ \text{CP} = \frac{18450 \times 100}{50} \]
\[ \text{CP} = \frac{1845000}{50} \]
\[ \text{CP} = 36900 \]

### Step 3: Determine the Selling Price for a Profit of 50%
To find the selling price (SP) for a profit of 50%, we use the formula:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
Substituting the values:
\[ \text{SP} = 36900 \times \left(1 + \frac{50}{100}\right) \]
\[ \text{SP} = 36900 \times \left(1 + 0.5\right) \]
\[ \text{SP} = 36900 \times 1.5 \]
\[ \text{SP} = 55350 \]

### Final Answer
Thus, the price at which he should have sold the article to earn a profit of 50% is **Rs. 55350**.

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