A trader gives 8% discount on the marked price of an article and gives 3 articles free for buying 18 articles and gains 38% in the entire transaction. Assuming a customer pays for 18 articles, the marked price of an article is what percent more than its cost price?

The correct option is 75%.

Let us understand the step-by-step derivation to find how much percent the marked price (MP) is more than the cost price (CP) of an article.

Step 1: Understand the Transaction Dynamics
The customer buys 18 articles and gets 3 articles free. This means the customer pays the marked price for 18 articles but receives a total of 18 + 3 = 21 articles.
From the trader's perspective:
The cost price is incurred on all 21 articles given away. Thus, the total Cost Price (CP_total) is:
${\mathrm{CP}}_{\mathrm{total}}=21\times \mathrm{CP}$
where CP is the cost price of a single article.

Step 2: Calculate the Selling Price
The trader charges for 18 articles at the marked price (MP) but gives an 8% discount on the marked price.
So, the selling price for one article paid for by the customer is:
$\mathrm{Selling\; Price\; per\; paid\; article}=\mathrm{MP}\times (1-0.08)=0.92\times \mathrm{MP}$
Since the customer pays for 18 articles, the total Selling Price (SP_total) received by the trader is:
${\mathrm{SP}}_{\mathrm{total}}=18\times 0.92\times \mathrm{MP}=16.56\times \mathrm{MP}$

Step 3: Relate Selling Price and Cost Price using the Profit Percentage
The trader gains 38% in the entire transaction. Therefore, the total Selling Price is 138% of the total Cost Price:
${\mathrm{SP}}_{\mathrm{total}}=1.38\times {\mathrm{CP}}_{\mathrm{total}}$
Substituting the expressions we found in Step 1 and Step 2:
$16.56\times \mathrm{MP}=1.38\times (21\times \mathrm{CP})$
$16.56\times \mathrm{MP}=28.98\times \mathrm{CP}$

Step 4: Find the Ratio of Marked Price to Cost Price
$\frac{\mathrm{MP}}{\mathrm{CP}}=\frac{28.98}{16.56}$
Dividing both numerator and denominator by 1.38 (or simplifying the decimal fraction):
$\frac{\mathrm{MP}}{\mathrm{CP}}=\frac{21}{12}=\frac{7}{4}=1.75$
This gives:
$\mathrm{MP}=1.75\times \mathrm{CP}$

Step 5: Calculate the Markup Percentage
The marked price is greater than the cost price by:
$\mathrm{Percentage\; Markup}=(\frac{\mathrm{MP}}{\mathrm{CP}}-1)\times 100$
$\mathrm{Percentage\; Markup}=(1.75-1)\times 100=0.75\times 100=75\%$

Thus, the marked price of an article is 75% more than its cost price.