An article is marked $40\%$ above the cost price. If a discount of $x\%$ is given on the marked price of the article, then a final profit of $12\%$ is obtained. Now if C.P. of a new article is $\text{Rs. }2,400$ and $x\%$ profit is desired then what should be the selling price of that new article?

Let the Cost Price ($\text{C.P.}$) of the original article be $100$.
Since the article is marked $40\%$ above the cost price:

$$\text{Marked Price (M.P.)}=100+40=140$$

A final profit of $12\%$ is obtained, so the Selling Price ($\text{S.P.}$) is:

$$\text{Selling Price (S.P.)}=100+12=112$$

The discount allowed on the marked price is:

$$\text{Discount}=\text{M.P.}-\text{S.P.}=140-112=28$$

The discount percentage ($x\%$) is calculated as:

$$x\%=\left(\frac{\text{Discount}}{\text{M.P.}}\right)\times 100\%=\left(\frac{28}{140}\right)\times 100\%=20\%$$

Thus, $x=20$.

Now, for the new article:

$$\text{C.P.}=\text{Rs. }2,400$$

Desired profit percentage = $x\%=20\%$

The selling price of the new article will be:

$$\text{New S.P.}=\text{C.P.}\times \left(1+\frac{\text{Profit}\%}{100}\right)$$

$$\text{New S.P.}=2,400\times \left(1+\frac{20}{100}\right)=2,400\times 1.2=\text{Rs. }2,880$$