Kartik sold an item for ₹ 6,500 and incurred a loss of 20%. At what price should he have sold the item to have gained a profit of20%?

Options

A. ₹10,375
B. ₹9,750
C. ₹8,125
D. Cannot be determined

Explanation

To solve the problem step by step, we will first determine the cost price (CP) of the item based on the selling price (SP) and the loss percentage. Then, we will calculate the selling price required to achieve a profit of 20%.

### Step 1: Determine the Cost Price (CP)
Given that Kartik sold the item for ₹6,500 at a loss of 20%, we can use the formula for selling price in terms of cost price and loss percentage:

\[ SP = CP - \text{Loss} \]

Since the loss is 20% of the cost price, we can express this as:

\[ SP = CP - 0.2 \times CP = 0.8 \times CP \]

Now, substituting the selling price:

\[ 6500 = 0.8 \times CP \]

To find the cost price (CP), we rearrange the equation:

\[ CP = \frac{6500}{0.8} \]

Calculating this gives:

\[ CP = 8125 \]

### Step 2: Calculate the Selling Price for a 20% Profit
Now that we have the cost price, we need to find the selling price that would yield a profit of 20%. The formula for selling price in terms of cost price and profit percentage is:

\[ SP = CP + \text{Profit} \]

The profit is 20% of the cost price:

\[ \text{Profit} = 0.2 \times CP \]

Substituting the cost price:

\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]

Now substituting the value of CP:

\[ SP = 1.2 \times 8125 \]

Calculating this gives:

\[ SP = 9750 \]

### Conclusion
Thus, to gain a profit of 20%, Kartik should have sold the item for ₹9,750.

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