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 one article be $\text{₹}1$.
The shopkeeper gives $1$ article free with $15$ articles, meaning he sells a total of $16$ articles.

$$\text{Total CP of 16 articles}=\text{₹}16$$

He gains $35\%$ on his total investment:

$$\text{Total Selling Price (SP)}=16\times 1.35=\text{₹}21.6$$

This total $\text{SP}$ is obtained from the customer paying for $15$ articles after a $4\%$ discount on the marked price ($\text{MP}$) of each article.
Let the $\text{MP}$ of one article be $M$.
The discounted price of one article $=M\times (1-0.04)=0.96M$.
The customer pays for $15$ articles:

$$\text{Total SP}=15\times 0.96M=14.4M$$

Equating the two expressions for Total $\text{SP}$:

$$14.4M=21.6$$

$$M=\frac{21.6}{14.4}=\frac{3}{2}=1.5$$

So, the $\text{MP}$ of one article is $\text{₹}1.5$, while its $\text{CP}$ is $\text{₹}1$.

$$\text{Percentage by which MP is above CP}=\left(\frac{1.5-1}{1}\times 100\right)\%=50\%$$