Correct Option (C)

Let the cost price of the article be 'C'.

According to the problem statement, the percentage profit when the article is sold at Rs 40 is equal to the percentage loss when it is sold at Rs 20.

Profit percentage is calculated as $\frac{Selling Price - Cost Price}{Cost Price} \times 100$ .
Loss percentage is calculated as $\frac{Cost Price - Selling Price}{Cost Price} \times 100$ .

Given that Profit% = Loss%, we can set up the equation:

$\frac{40 - C}{C} \times 100 = \frac{C - 20}{C} \times 100$

Simplifying the equation by dividing both sides by 100 and multiplying by C (since C cannot be zero):

$40 - C = C - 20$

Rearranging the terms to solve for C:

$40 + 20 = C + C$

$60 = 2 C$

$C = \frac{60}{2}$

$C = 30$

Therefore, the original cost of the article is Rs 30.

Incorrect Options:

Option A (Rs 10): If the cost price is Rs 10, selling at Rs 40 results in a profit of Rs 30 (300% profit). Selling at Rs 20 results in a profit of Rs 10 (100% profit). This contradicts the condition of incurring a loss when sold at Rs 20 and having equal percentages.
Option B (Rs 20): If the cost price is Rs 20, selling at Rs 40 results in a profit of Rs 20 (100% profit). Selling at Rs 20 results in no profit or loss (0%). This contradicts the condition of equal percentages of profit and loss.
Option D (Rs 40): If the cost price is Rs 40, selling at Rs 40 results in no profit or loss (0%). Selling at Rs 20 results in a loss of Rs 20 (50% loss). This contradicts the condition of equal percentages of profit and loss.