A trader allows a discount of $20\%$ on the marked price. He still has a profit of $44\%$ on the cost price. Find the profit percentage if he sells at the marked price.

Let the Cost Price ($\text{CP}$) be $\text{₹}100$.
Since the profit is $44\%$, the Selling Price ($\text{SP}$) is:

$$\text{SP}=100+44=\text{₹}144$$

The trader allows a discount of $20\%$ on the Marked Price ($\text{MP}$), which means the Selling Price is $80\%$ of the Marked Price:

$$80\%\text{ of MP}=144$$

$$0.8\times \text{MP}=144⟹\text{MP}=\frac{144}{0.8}=\text{₹}180$$

If he sells at the marked price, the new selling price becomes the marked price (${\text{SP}}_{\text{new}}=\text{MP}=\text{₹}180$).
The profit would be:

$$\text{Profit}={\text{SP}}_{\text{new}}-\text{CP}=180-100=\text{₹}80$$

$$\text{Profit }\%=\left(\frac{80}{100}\right)\times 100\%=80\%$$