The marked price of an article is $35\%$ more than its cost price. If a discount of $15\%$ is given, what will be the profit percentage?

Let the Cost Price ($\text{CP}$) of the article be $100$.
1. **Calculate the Marked Price ($\text{MP}$):**
Since the marked price is $35\%$ more than the cost price:

$$\text{MP}=100+35=135$$

2. **Calculate the Selling Price ($\text{SP}$) after a $15\%$ discount:**

$$\text{Discount}=15\%\text{ of }135=\frac{15}{100}\times 135=20.25$$

$$\text{SP}=\text{MP}-\text{Discount}=135-20.25=114.75$$

3. Calculate the Profit Percentage:

$$\text{Profit}=\text{SP}-\text{CP}=114.75-100=14.75$$

$$\text{Profit Percentage}=14.75\%=14\frac{75}{100}\%=14\frac{3}{4}\%$$