Raj sold an item for ₹6,384 and incurred a loss of 30%. At what price should he have sold the Item to have gamed a profit of 30%?

Options

A. ₹14,656
B. ₹11,856
C. ₹13,544
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 incurred. Then, we will calculate the selling price needed to achieve a profit of 30%.

### Step 1: Determine the Selling Price (SP) and Loss Percentage
Given:
- Selling Price (SP) = ₹6,384
- Loss Percentage = 30%

### Step 2: Calculate the Cost Price (CP)
Since Raj incurred a loss of 30%, it means he sold the item for 70% of its cost price (CP). We can express this relationship as:

\[ SP = CP \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \]

Substituting the values we have:

\[ 6384 = CP \times \left(1 - \frac{30}{100}\right) \]
\[ 6384 = CP \times 0.7 \]

Now, we can solve for CP:

\[ CP = \frac{6384}{0.7} \]
\[ CP = 9112.86 \]

### Step 3: Calculate the Selling Price for a Profit of 30%
To find the selling price (SP') for a profit of 30%, we use the formula:

\[ SP' = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Substituting the values:

\[ SP' = 9112.86 \times \left(1 + \frac{30}{100}\right) \]
\[ SP' = 9112.86 \times 1.3 \]
\[ SP' = 11846.71 \]

### Final Answer:
Raj should have sold the item for approximately ₹11,846.71 to gain a profit of 30%.

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