A man sold an article at a loss of $20\%$. If he could sell it for $\text{₹}1,200$ more, he would make a profit of $5\%$. What is the cost price of the article?

Let the Cost Price ($\text{CP}$) of the article be $100\%$.
* Initially, the article is sold at a loss of $20\%$, so the initial Selling Price (${\text{SP}}_1$) is $100\%-20\%=80\%$.
* If it is sold for $\text{₹}1,200$ more, the new profit would be $5\%$, so the new Selling Price (${\text{SP}}_2$) is $100\%+5\%=105\%$.

The difference between the two selling prices is:

$${\text{SP}}_2-{\text{SP}}_1=105\%-80\%=25\%$$

This $25\%$ difference is equal to $\text{₹}1,200$:

$$25\%\text{ of CP}=\text{₹}1,200$$

To find the cost price ($100\%$):

$$\text{CP}=\frac{1,200}{25}\times 100=1,200\times 4=\text{₹}4,800$$