A merchant purchased a digital camera at a discount of 25% on its marked price and subsequently sold it at a loss of 20% relative to their purchase cost. What would have been the percentage loss if the merchant had bought the camera at its marked price?

The correct answer is 40%.

Step 1: Determine the purchase cost (Cost Price).
Let us assume the marked price (MP) of the digital camera is 100 units.

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

The merchant purchased the camera at a discount of 25% on its marked price:
$\text{Discount}=25\%\text{of}100=25$

Therefore, the merchant's purchase cost (Cost Price, CP) is:
$\text{Cost Price (CP)}=\text{MP}-\text{Discount}=100-25=75$

Step 2: Determine the selling price (SP).
The merchant sold the camera at a loss of 20% relative to their purchase cost (CP):
$\text{Loss}=20\%\text{of}75=\frac{20}{100}\times 75=15$

Thus, the selling price (SP) is:
$\text{Selling Price (SP)}=\text{CP}-\text{Loss}=75-15=60$

Step 3: Calculate the percentage loss if bought at the marked price.
If the merchant had purchased the camera at its marked price without any discount, the new cost price would be:
$\text{New Cost Price}=\text{MP}=100$

The selling price remains 60 units. So, the new loss incurred would be:
$\text{New Loss}=\text{New Cost Price}-\text{Selling Price}=100-60=40$

Now, calculate the percentage loss based on this new cost price:
$\text{Percentage Loss}=\left(\frac{\text{New Loss}}{\text{New Cost Price}}\right)\times 100\%=\left(\frac{40}{100}\right)\times 100\%=40\%$

Hence, the percentage loss would have been 40%.