A shopkeeper sells an article at ₹ 40 and gets X% profit. However, when he sells it at ₹ 20, he faces same percentage of loss. What is the original cost of the article?

The correct option is ₹ 30.

Let the original cost price of the article be $\mathrm{CP}$.

Step 1: Understand the Profit Case
When the shopkeeper sells the article at ₹ 40, he makes a profit of $X\%$.
The formula for profit percentage is:
$\mathrm{Profit}\%=\frac{\mathrm{Selling\; Price\; (SP)}-\mathrm{Cost\; Price\; (CP)}}{\mathrm{CP}}\times 100$
Given that the selling price is ₹ 40 and the profit percentage is $X\%$, we can write:
$X=\frac{40-\mathrm{CP}}{\mathrm{CP}}\times 100$ ---- (Equation 1)

Step 2: Understand the Loss Case
When the shopkeeper sells the article at ₹ 20, he faces the same percentage of loss, which is $X\%$.
The formula for loss percentage is:
$\mathrm{Loss}\%=\frac{\mathrm{Cost\; Price\; (CP)}-\mathrm{Selling\; Price\; (SP)}}{\mathrm{CP}}\times 100$
Given that the selling price is ₹ 20 and the loss percentage is $X\%$, we can write:
$X=\frac{\mathrm{CP}-20}{\mathrm{CP}}\times 100$ ---- (Equation 2)

Step 3: Equate the two expressions for X
Since the profit percentage and loss percentage are both equal to $X$, we can equate Equation 1 and Equation 2:
$\frac{40-\mathrm{CP}}{\mathrm{CP}}\times 100=\frac{\mathrm{CP}-20}{\mathrm{CP}}\times 100$

We can simplify this equation by dividing both sides by 100 and multiplying both sides by $\mathrm{CP}$:
$40-\mathrm{CP}=\mathrm{CP}-20$

Now, rearrange the terms to solve for $\mathrm{CP}$:
$40+20=\mathrm{CP}+\mathrm{CP}$
$60=2\mathrm{CP}$
$\mathrm{CP}=\frac{60}{2}$
$\mathrm{CP}=30$

Therefore, the original cost price of the article is ₹ 30.