Final answer:
To determine the cost price of an item with a marked price of 200, after a 20% discount and a 25% profit, we calculate the selling price after the discount (160) and then find the cost price to be 128. The given options do not match this answer.
Step-by-step explanation:
The question asks us to calculate the cost price of an article with a marked price of 200, given that a shopkeeper offers a 20% discount and still makes a 25% profit. To find the cost price, we must first determine the selling price after the discount and then use the profit percentage to calculate the cost price.
Step 1: Calculate the selling price after the discount. A 20% discount on a marked price of 200 is 200 x 0.20 = 40. Therefore, the selling price is 200 - 40 = 160.
Step 2: If the shopkeeper makes a 25% profit, the cost price (C) can be found by the equation C + 0.25C = Selling Price. Given that the selling price is 160, we have C + 0.25C = 160, which simplifies to 1.25C = 160. To find C, we divide 160 by 1.25, giving us a cost price of 128.
Thus, the cost price of the article is 128, which is not one of the options provided (a) 140, (b) 150, (c) 160, (d) 170, indicating a possible typo or mistake in the question or the options.