A retailer bought $7$ articles for $\text{Rs. }10$ each, $9$ articles for $\text{Rs. }11$ each, and $14$ articles for $\text{Rs. }15each$. Find the selling price per article if the profit is supposed to be $20\%$ of the average cost price.

Let's first calculate the total cost price (CP) of all the articles:
$$\text{Total CP}=(7\times 10)+(9\times 11)+(14\times 15)$$

$$\text{Total CP}=70+99+210=\text{Rs. }379$$

Total number of articles bought:

$$\text{Total Articles}=7+9+14=30$$

Now, find the average cost price per article:

$$\text{Average CP}=\frac{379}{30}$$

The required profit is $20\%$ of the average cost price. Therefore, the selling price (SP) per article will be $120\%$ of the average cost price:

$$\text{SP per article}=\text{Average CP}\times \left(1+\frac{20}{100}\right)=\frac{379}{30}\times 1.2$$

$$\text{SP per article}=\frac{379}{30}\times \frac{12}{10}=\frac{379\times 4}{100}=\frac{1516}{100}=\text{Rs. }15.16$$