If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensure that she makes a profit of 20%?

Options

A. give a discount of 5% on retail price.
B. give a discount of 2% on retail price
C. Increase the retail price by 2%
D. Sell at retail price

Answer

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

### Step 1: Understand the given information
The seller gives a discount of 15% on the retail price and still makes a profit of 2%. We need to find out how to ensure a profit of 20%.

### Step 2: Assume the retail price (RP)
Let’s assume the retail price (RP) is 100.

### Step 3: Calculate the selling price (SP) after discount
The discount given is 15% of the retail price:
\[ \text{Discount} = 15\% \text{ of } 100 = 15 \]
Thus, the selling price (SP) after the discount is:
\[ \text{SP} = \text{RP} - \text{Discount} = 100 - 15 = 85 \]

### Step 4: Relate selling price to cost price (CP)
The seller makes a profit of 2% on the cost price. Therefore, we can express the selling price in terms of the cost price:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{2}{100}\right) \]
This means:
\[ 85 = \text{CP} \times \frac{102}{100} \]

### Step 5: Solve for the cost price (CP)
To find the cost price, rearrange the equation:
\[ \text{CP} = \frac{85 \times 100}{102} \]
Calculating this gives:
\[ \text{CP} = \frac{8500}{102} \approx 83.33 \]

### Step 6: Calculate the new selling price for a 20% profit
To ensure a profit of 20%, we need to calculate the new selling price (SP') based on the cost price:
\[ \text{SP'} = \text{CP} \times \left(1 + \frac{20}{100}\right) \]
Substituting the value of CP:
\[ \text{SP'} = 83.33 \times \frac{120}{100} = 83.33 \times 1.2 = 100 \]

### Step 7: Conclusion
The new selling price to ensure a profit of 20% is 100. Since the retail price is also 100, selling at the retail price ensures a 20% profit.

### Final Answer
The correct option is to sell at the retail price of 100.

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