\text{By selling an article at }\frac{6}{15}\text{ of its actual selling price, Hitesh incurs a loss of}\mathrm{ 28}\%\text{. If he sells it at}89\%\text{of its actual selling price, then the profit percentage is}

The correct option is 60.2%.

Let us solve this problem step-by-step to understand the logic behind finding the profit percentage.

Step 1: Define the variables

Let the actual selling price of the article be $SP$ and the cost price of the article be $CP$.

Step 2: Use the first given condition

Hitesh sells the article at $\frac{6}{15}$ of its actual selling price, which means the new selling price ($S{P}_1$) is:

$S{P}_1=\frac{6}{15}\times SP=\frac{2}{5}SP=0.4\times SP$

At this selling price, he incurs a loss of 28%. This means the selling price is 72% (100% - 28%) of the cost price $CP$:

$S{P}_1=0.72\times CP$

Equating the two expressions for $S{P}_1$:

$0.4\times SP=0.72\times CP$

$SP=\frac{0.72}{0.4}\times CP=1.8\times CP$

Step 3: Use the second given condition

Now, Hitesh sells the article at 89% of its actual selling price. Thus, the new selling price ($S{P}_2$) is:

$S{P}_2=89\%\times SP=0.89\times SP$

Substitute $SP=1.8\times CP$ into the equation:

$S{P}_2=0.89\times (1.8\times CP)=1.602\times CP$

Step 4: Calculate the Profit Percentage

Since $S{P}_2=1.602\times CP$, the selling price is 160.2% of the cost price.

The profit percentage is given by:

$\text{Profit \%}=\frac{S{P}_2-CP}{CP}\times 100$

$\text{Profit \%}=\frac{1.602\times CP-CP}{CP}\times 100=0.602\times 100=60.2\%$

Therefore, the profit percentage is 60.2%.