A tradesman gives a $4\%$ discount on the marked price and gives an article free for buying every 15 articles and thus gains $35\%$. Find out by what percentage the marked price is above the cost price.

Let the Cost Price ($\text{CP}$) of each article be ₹$x$.
The tradesman sells 15 articles but gives 16 articles in total (15 + 1 free).
Therefore, the total cost price for 16 articles = $16x$.

He makes a profit of $35\%$. Thus, the total Selling Price ($\text{SP}$) is:

$$\text{Total SP}=16x\times \left(1+\frac{35}{100}\right)=16x\times 1.35=21.6x$$

This total selling price is obtained from selling 15 articles after a discount of $4\%$ on the Marked Price ($\text{MP}$) of each article.

$$\text{Total SP}=15\times \text{MP}\times \left(1-\frac{4}{100}\right)$$

$$21.6x=15\times \text{MP}\times 0.96$$

$$21.6x=14.4\times \text{MP}$$

$$\text{MP}=\frac{21.6x}{14.4}=1.5x$$

The percentage by which the marked price is above the cost price is:

$$\text{Percentage Increase}=\frac{\text{MP}-\text{CP}}{\text{CP}}\times 100$$

$$\text{Percentage Increase}=\frac{1.5x-x}{x}\times 100=0.5\times 100=50\%$$