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

Let CP be the original cost of the article. Let X be the percentage profit or loss.

1. When the article is sold at Rs. 40, there is X% profit. This can be written as: 40 = CP * (1 + X/100) (Equation 1)

2. When the article is sold at Rs. 20, there is X% loss. This can be written as: 20 = CP * (1 - X/100) (Equation 2)

To find CP, we can divide Equation 1 by Equation 2: 40 / 20 = [CP * (1 + X/100)] / [CP * (1 - X/100)] 2 = (1 + X/100) / (1 - X/100)

Now, solve for X: 2 * (1 - X/100) = 1 + X/100 2 - 2X/100 = 1 + X/100 Subtract 1 from both sides: 1 - 2X/100 = X/100 Add 2X/100 to both sides: 1 = X/100 + 2X/100 1 = 3X/100 X = 100/3

Now substitute the value of X back into Equation 2 (or Equation 1): 20 = CP * (1 - (100/3)/100) 20 = CP * (1 - 1/3) 20 = CP * (2/3) CP = 20 * (3/2) CP = 30

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

Alternatively, a useful property states that if an article is sold at two different prices, yielding the same percentage of profit and loss respectively, then the Cost Price (CP) is the average of the two selling prices (SP1 and SP2). CP = (SP1 + SP2) / 2 CP = (40 + 20) / 2 CP = 60 / 2 CP = 30

Analysis of options: A) Rs. 10: If CP=10, profit at SP=40 is (40-10)/10 = 300%. Loss at SP=20 is (10-20)/10 = -100% (100% loss). Percentages are not equal. B) Rs. 20: If CP=20, profit at SP=40 is (40-20)/20 = 100%. Loss at SP=20 is (20-20)/20 = 0%. Percentages are not equal. C) Rs. 30: If CP=30, profit at SP=40 is (40-30)/30 = 10/30 = 33.33%. Loss at SP=20 is (30-20)/30 = 10/30 = 33.33%. Percentages are equal. This is correct. D) Rs. 40: If CP=40, profit at SP=40 is (40-40)/40 = 0%. Loss at SP=20 is (40-20)/40 = 50%. Percentages are not equal.

The final answer is C) Rs. 30.