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%.

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first and then determine the selling price (SP) required to achieve a profit of 25%.

### Step 1: Set up the equations based on the given information.
Let the cost price (CP) of the article be Rs. x.

When the article is sold for Rs. 800, the profit is given by:
\[ \text{Profit} = \text{SP} - \text{CP} = 800 - x \]

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

According to the problem, the profit earned when sold for Rs. 800 is 20 times the loss incurred when sold for Rs. 275:
\[ 800 - x = 20 \times (x - 275) \]

### Step 2: Solve the equation for CP (x).
Expanding the equation:
\[ 800 - x = 20x - 5500 \]

Now, rearranging the equation:
\[ 800 + 5500 = 20x + x \]
\[ 6300 = 21x \]

Now, divide both sides by 21 to find CP:
\[ x = \frac{6300}{21} = 300 \]

### Step 3: Calculate the selling price for a 25% profit.
To find the selling price that gives a profit of 25%, we calculate:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where profit is 25% of CP:
\[ \text{Profit} = 0.25 \times \text{CP} = 0.25 \times 300 = 75 \]

Now, substituting the values:
\[ \text{SP} = 300 + 75 = 375 \]

### Conclusion:
The article should be sold for Rs. 375 to achieve a profit of 25%.

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