Suhas sold an item for Rs. 7,500 /- and incurred a loss of 25%. At what price should he have sold the item to have gained a profit of 25% ?

Options

A. Rs. 13,800 /-
B. Rs. 12,500 /-
C. Rs. 11,200 /-
D. Cannot be determined

Answer

To solve the problem step by step, we need to find out the cost price (CP) of the item first, and then determine the selling price (SP) that would provide a profit of 25%.

### Step 1: Find the Cost Price (CP)
Given that Suhas sold the item for Rs. 7,500 and incurred a loss of 25%, we can use the formula for selling price in terms of cost price and loss percentage:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss} \]

Since the loss is 25%, we can express it as:

\[ \text{Loss} = \frac{25}{100} \times \text{CP} = 0.25 \times \text{CP} \]

Thus, we can rewrite the selling price equation as:

\[ 7500 = \text{CP} - 0.25 \times \text{CP} \]

This simplifies to:

\[ 7500 = 0.75 \times \text{CP} \]

Now, we can solve for CP:

\[ \text{CP} = \frac{7500}{0.75} = 10000 \]

### Step 2: Calculate the Selling Price for a Profit of 25%
Now that we have the cost price (CP) as Rs. 10,000, we can find out the selling price (SP) that would yield a profit of 25%. The formula for selling price in terms of cost price and profit percentage is:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

The profit can be calculated as:

\[ \text{Profit} = \frac{25}{100} \times \text{CP} = 0.25 \times 10000 = 2500 \]

Now substituting the values into the SP formula:

\[ \text{SP} = 10000 + 2500 = 12500 \]

### Final Answer
Suhas should have sold the item for Rs. 12,500 to gain a profit of 25%.

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