A trader gives 10% discount on the marked price of an article and gives 40 articles free for buying 112 articles and gains 26% in the entire transaction. Assuming a customer pays for 112 articles, the marked price of an article is what percentage more than its cost price?

Correct Answer: 90%

Let's break down the given problem step-by-step to find the percentage by which the marked price exceeds the cost price.

Step 1: Understand the transaction details
Let the Cost Price (CP) of 1 article be $c$.
Let the Marked Price (MP) of 1 article be $m$.

The customer pays for 112 articles and gets 40 articles free.
Therefore, total articles given by the trader = 112 + 40 = 152 articles.

Step 2: Calculate Total Cost Price and Total Selling Price
The trader actually incurs a cost for all 152 articles given out:
Total Cost Price (CP) = 152 $\times$ $c$

The customer pays the discounted marked price for only 112 articles.
A discount of 10% is given on the marked price, so the selling price per paid article is 90% of $m$, which is 0.9$m$.
Total Selling Price (SP) = 112 $\times$ 0.9$m$ = 100.8$m$

Step 3: Relate SP and CP using the profit percentage
The trader gains 26% overall in the entire transaction.
Therefore, Total SP = 126% of Total CP

$100.8m=1.26\times 152c$

$100.8m=191.52c$

Now, let's find the ratio of Marked Price ($m$) to Cost Price ($c$):

$\frac{m}{c}=\frac{191.52}{100.8}=1.9$

Step 4: Calculate the required percentage
Since $m=1.9c$, the marked price is 1.9 times the cost price, or 190% of the cost price.

Percentage by which MP is more than CP = (1.9 - 1) $\times$ 100% = 0.9 $\times$ 100% = 90%

Hence, the marked price of an article is 90% more than its cost price.