Priya buys a dress at a discount of `20%`. At what percentage above the cost price should she sell it to make a profit of `30%` over the original list price ?

Options

A. `35%`
B. `60%`
C. `62.5%`
D. None of these

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
Priya buys a dress at a discount of 20%. We need to find out at what percentage above the cost price she should sell it to make a profit of 30% over the original list price.

### Step 2: Assume the Original List Price
Let’s assume the original list price (LP) of the dress is Rs. 100. This makes calculations easier.

### Step 3: Calculate the Cost Price (CP)
Since Priya buys the dress at a discount of 20%, we can calculate the cost price (CP) as follows:
\[ CP = LP - \text{Discount} \]
\[ \text{Discount} = 20\% \text{ of } 100 = 20 \]
\[ CP = 100 - 20 = 80 \]

### Step 4: Calculate the Selling Price (SP) for Desired Profit
Priya wants to make a profit of 30% over the original list price. Therefore, we calculate the selling price (SP) as follows:
\[ SP = LP + \text{Profit} \]
\[ \text{Profit} = 30\% \text{ of } 100 = 30 \]
\[ SP = 100 + 30 = 130 \]

### Step 5: Calculate the Profit Percentage over Cost Price
Now we need to find out at what percentage above the cost price (CP) she should sell it to achieve this selling price (SP). The formula for profit percentage is:
\[ \text{Profit Percentage} = \frac{SP - CP}{CP} \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \frac{130 - 80}{80} \times 100 \]
\[ = \frac{50}{80} \times 100 \]
\[ = \frac{5000}{80} \]
\[ = 62.5\% \]

### Final Answer
Priya should sell the dress at **62.5%** above the cost price to make a profit of 30% over the original list price.

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