The Problem:
The selling price of 16 pens is the same as the cost price of 25 pens. The total discount offered on 50 pens is equal to the selling price of 14 pens. We need to find out the markup percentage.

Understanding the Problem:
To solve this problem, we need to understand the concepts of selling price, cost price, discount, and markup percentage.

- Selling Price (SP): The price at which a product is sold to the customer.
- Cost Price (CP): The price at which a product is purchased or manufactured.
- Discount: The reduction in price offered on a product.
- Markup Percentage: The percentage by which the selling price exceeds the cost price.

Given Information:
Let's summarize the given information:
- Selling price of 16 pens = Cost price of 25 pens
- Total discount on 50 pens = Selling price of 14 pens

Calculating the Markup Percentage:
To find the markup percentage, we need to calculate the difference between the selling price and the cost price, and then express it as a percentage of the cost price.

Step 1: Calculate the Selling Price of 16 pens:
Since the selling price of 16 pens is equal to the cost price of 25 pens, we can set up the following equation:
16(SP) = 25(CP)

Step 2: Calculate the Selling Price of 1 pen:
To find the selling price of 1 pen, we can divide both sides of the equation by 16:
SP = (25/16)CP

Step 3: Calculate the Selling Price of 50 pens:
To find the selling price of 50 pens, we can multiply both sides of the equation by 50:
50(SP) = (25/16)CP * 50

Step 4: Calculate the Discount on 50 pens:
The total discount on 50 pens is equal to the selling price of 14 pens. Therefore, we can set up the following equation:
Discount = 14(SP)

Step 5: Calculate the Markup Percentage:
Since markup percentage is the difference between the selling price and the cost price expressed as a percentage of the cost price, we can calculate it using the following formula:
Markup Percentage = ((SP - CP) / CP) * 100

Step 6: Substitute the Values:
Now, let's substitute the calculated values into the formula to find the markup percentage:
Markup Percentage = ((50(SP) - 50(CP)) / 50(CP)) * 100

Step 7: Simplify the Equation:
Using the previously calculated equations, we can simplify the markup percentage equation as follows:
Markup Percentage = (((25/16)CP - CP) / CP) * 100
Markup Percentage = (((25/16) - 1) / 1) * 100
Markup Percentage = (9/16) * 100
Markup Percentage = 56.25

Conclusion:
The markup percentage is equal to 56.25%. However, this answer does not match the given correct answer of 100%. Therefore, there might be an error in the solution or the given correct answer.