Let's solve this using the assumption method step by step.

Step 1: Assume the cost price

Assume the cost price (C.P.) of the goods is $100.

Step 2: Let the marked price be "x"

Let the marked price (M.P.) of the goods be $x.

Step 3: Apply the discount

The merchant offers a 40% discount on the marked price. Therefore, the selling price (S.P.) is: $S.P. = M.P. - 40\% \text{ of M.P.} = x - 0.4x = 0.6x$

Step 4: Selling at cost price

According to the problem, the merchant ends up selling at the cost price, meaning: $S.P. = C.P.$ So, we have: $0.6x = 100$

Step 5: Solve for the marked price

Now, solve for $x$ (the marked price): $x = \frac{100}{0.6} = 166.67$

Step 6: Calculate the markup percentage

The markup is the difference between the marked price and the cost price, which is: $\text{Markup} = M.P. - C.P. = 166.67 - 100 = 66.67$ The markup percentage is: $\text{Markup Percentage} = \left( \frac{\text{Markup}}{C.P.} \right) \times 100 = \left( \frac{66.67}{100} \right) \times 100 = 66.67\%$

Conclusion

The markup percentage is 66.67%.

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Would you like more details or have any questions?

Here are five questions you might consider next:

1. How do different discount percentages affect the markup needed to sell at cost price?
2. What happens if the merchant offers a higher discount than 40%? How would that affect the markup?
3. How would this calculation change if the cost price was something other than $100?
4. How does the selling price relate to profit margins in different pricing strategies?
5. What would be the markup percentage if the discount offered was 30% instead of 40%?

Tip: To avoid losses, always ensure that the selling price covers both the cost price and any additional business expenses.