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%?

The correct option is D.

Let the cost price of the article be $C$ and the retail price (marked price) be $R$.

Giving a discount of 15% on the retail price means the selling price is:
$\text{SP}=0.85R$

Since she makes a profit of 2%, the selling price is also equal to:
$\text{SP}=1.02C$

Equating the two expressions for the selling price:
$0.85R=1.02C$
$R=\frac{1.02}{0.85}C$
$R=\frac{6}{5}C=1.20C$

This shows that the retail price is exactly 120% of the cost price. If she sells the product at the retail price, she will make a profit of 20%.

To ensure a profit of exactly 20%, she must sell the article at the retail price $R$, which corresponds to a 0% discount on the retail price.

Let's double-check the options to see which matches this requirement:

• Option A: A discount of 5% on retail price gives $\text{SP}=0.95R=0.95\times 1.2C=1.14C$ (14% profit).
• Option B: A discount of 2% on retail price gives $\text{SP}=0.98R=0.98\times 1.2C=1.176C$ (17.6% profit).
• Option C: Increasing the retail price by 2% doesn't directly target selling at the base retail price unless details of the transaction discount are given.
• Option D: Sell at retail price gives , which ensures exactly 20% profit.

Wait, let's re-verify the calculation. We have:

$\frac{R}{C}$

Thus, $R=1.20C$. The retail price is exactly 20% above the cost price. Therefore, selling the item at the retail price (0% discount) results in a profit of exactly 20%.