Question

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

• 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 1

The Correct Option is D

Step 1: Definitions

Let: \[ R = \text{Retail Price}, \quad C = \text{Cost Price} \]

Step 2: Current scenario

A 15% discount is given, so: \[ SP_{\text{current}} = R - 0.15R = 0.85R \] We are told this yields a profit of 2%, so: \[ SP_{\text{current}} = C + 0.02C = 1.02C \] Equating: \[ 0.85R = 1.02C \] Thus: \[ C = \frac{0.85}{1.02}R \]

Step 3: Desired scenario

We now want a profit of 20%, so: \[ SP_{\text{desired}} = C + 0.20C = 1.20C \] Substitute \( C = \frac{0.85}{1.02}R \): \[ SP_{\text{desired}} = 1.20 \times \frac{0.85}{1.02}R \] \[ SP_{\text{desired}} = \frac{1.02R}{1.02} = R \]

Step 4: Conclusion

The desired selling price equals the retail price \( R \), which means no discount is required to achieve a 20% profit.

Final Answer:

\[ \boxed{\text{Sell at retail price (0\% discount)}} \]