An article was sold for $\text{Rs. }2,288$ at a discount of $20\%$ after $2$ successive mark-ups of $10\%$ and $30\%$. Find the cost price of the article.

Let the cost price (CP) of the article be $x$.
After two successive mark-ups of $10\%$ and $30\%$, the Marked Price (MP) becomes:

$$\text{MP}=x\times \left(1+\frac{10}{100}\right)\times \left(1+\frac{30}{100}\right)$$

$$\text{MP}=x\times 1.1\times 1.3=1.43x$$

A discount of $20\%$ is given on the Marked Price to compute the Selling Price (SP):

$$\text{SP}=\text{MP}\times \left(1-\frac{20}{100}\right)$$

$$\text{SP}=1.43x\times 0.8=1.144x$$

Given that the Selling Price is $\text{Rs. }2,288$:

$$1.144x=2,288$$

$$x=\frac{2,288}{1.144}=2,000$$

Thus, the cost price of the article is $\text{Rs. }2,000$.