An article is marked up by Rs. X and the cost price of the article is Rs. 28000. If discount of Rs. is given and he gets a profit of 12.5%, then find X/2.

Sure, let's solve the problem step by step.

Step 1: Let's assume the markup amount is Rs. X.

Step 2: The cost price of the article is given as Rs. 28000.

Step 3: A discount of Rs. is given. We need the value of the discount to proceed with the calculation.

Step 4: After applying the discount, the selling price of the article can be calculated using the formula:

Selling Price = Cost Price - Discount

Step 5: We are given that the selling price results in a profit of 12.5%. To calculate the selling price, we can use the formula:

Selling Price = Cost Price + Profit

Step 6: Now, we can equate the two formulas for the selling price:

Cost Price - Discount = Cost Price + Profit

Step 7: Simplifying the equation, we get:

-Discount = Profit

Step 8: We know that profit is calculated as a percentage of the cost price. In this case, the profit is 12.5% of the cost price. So, we can write:

Profit = 12.5% of Cost Price

Step 9: Converting the percentage to a decimal, we have:

Profit = 0.125 * Cost Price

Step 10: Substituting the given cost price of Rs. 28000, we can calculate the profit:

Profit = 0.125 * 28000

Step 11: Calculating the profit, we find:

Profit = Rs. 3500

Step 12: Now, we can substitute the value of the profit into the equation from Step 7:

-Discount = Rs. 3500

Step 13: Solving for the discount, we find:

Discount = -Rs. 3500

Step 14: Since the discount is given as a negative value, it means that the article is marked up by Rs. X.

Step 15: We need to find X/2. Since X is the markup amount, we can calculate X/2 as:

X/2 = (Markup Amount)/2

Step 16: Substituting the value of the markup amount, we have:

X/2 = (Rs. X)/2

Therefore, X/2 is equal to Rs. X/2.

Please note that the value of X is not provided in the given information, so we cannot calculate the exact value of X/2.