A man makes a profit of $20\%$ on selling $20$ articles for $\text{Re. }1$. The number of articles he bought by $\text{Re. }1$ is

Given that Selling Price ($\text{SP}$) of $20$ articles $=\text{Re. }1$.
$$\text{SP of 1 article}=\text{Re. }\frac{1}{20}$$

The profit rate is $20\%$. We compute the Cost Price ($\text{CP}$) of a single article using the pricing formula:

$$\text{CP}=\frac{\text{SP}}{1+\frac{\text{Profit}\%}{100}}$$

$$\text{CP of 1 article}=\frac{\frac{1}{20}}{1+0.20}=\frac{1}{20\times 1.2}=\text{Re. }\frac{1}{24}$$

Since the cost price of one article is $\text{Re. }\frac{1}{24}$, the number of articles he purchased for $\text{Re. }1$ is exactly $24$.