The profit earned when an article is sold for Rs. 800 is 20 times the loss incurred when it is sold for Rs. 275. At what price should the article be sold if it is desired to make a profit of 25%?

Options

A. Rs. 300
B. Rs. 350
C. Rs. 375
D. Rs. 400

Answer

To solve the problem step by step, we need to find the cost price of the article first and then determine the selling price that would yield a profit of 25%.

### Step 1: Define the variables
Let the cost price (CP) of the article be denoted as \( CP \).

### Step 2: Set up the profit and loss equations
According to the problem:
- When the article is sold for Rs. 800, the profit is given by:
\[ \text{Profit} = 800 - CP \]

- When the article is sold for Rs. 275, the loss is given by:
\[ \text{Loss} = CP - 275 \]

### Step 3: Relate profit and loss
The problem states that the profit when sold for Rs. 800 is 20 times the loss when sold for Rs. 275:
\[ 800 - CP = 20 \times (CP - 275) \]

### Step 4: Expand and rearrange the equation
Expanding the equation gives:
\[ 800 - CP = 20CP - 5500 \]
Rearranging this, we get:
\[ 800 + 5500 = 20CP + CP \]
\[ 6300 = 21CP \]

### Step 5: Solve for the cost price
Now, we can solve for \( CP \):
\[ CP = \frac{6300}{21} = 300 \]

### Step 6: Calculate the selling price for a 25% profit
To find the selling price (SP) for a desired profit of 25%, we use the formula:
\[ SP = CP + \left(\frac{25}{100} \times CP\right) \]
This can be simplified to:
\[ SP = CP \times \left(1 + \frac{25}{100}\right) = CP \times 1.25 \]
Substituting \( CP = 300 \):
\[ SP = 300 \times 1.25 = 375 \]

### Final Answer
Thus, the article should be sold for Rs. 375 to achieve a profit of 25%.

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