A bought the article at a discount of 20% on the Marked price and then sold the article with a 10% loss. What would have been the percentage loss had he bought it at the marked price?

The correct option is 28%.

Let's solve the problem step-by-step by calculating the marked price, cost price, selling price, and the required percentage loss.

Step 1: Assume a Marked Price (MP) for the article.
Let the Marked Price of the article be:

$\text{Marked Price (MP)}=100$

Step 2: Calculate the purchasing price (Cost Price for A).
A bought the article at a discount of 20% on the Marked Price.
Discount amount = 20% of 100 = 20.

$\text{Cost Price (CP)}=100-20=80$

Step 3: Calculate the Selling Price (SP) when sold at a 10% loss.
A sold the article at a 10% loss on his purchasing cost (CP).
Loss amount = 10% of 80 = 8.

$\text{Selling Price (SP)}=80-8=72$

Step 4: Determine the percentage loss if bought at the Marked Price.
If he had bought the article at the Marked Price (MP = 100) instead of the discounted price, his new Cost Price would be 100 while the Selling Price remains 72.
New Loss = New Cost Price - Selling Price

$\text{New Loss}=100-72=28$

Now, compute the new percentage loss:

$\text{Percentage Loss}=\left(\frac{\text{New Loss}}{\text{New Cost Price}}\right)\times 100$

$\text{Percentage Loss}=\left(\frac{28}{100}\right)\times 100=28\%$

Therefore, the percentage loss had he bought it at the marked price would have been 28%.