To determine the percentage discount a merchant can offer on the marked price to either end up with no profit or loss, we can break the problem down as follows:

1. Marked price: The merchant marks up his goods by 40%. This means that if the cost price (CP) is $C$, the marked price (MP) will be:

   $MP = C + 40\% \text{ of } C = C + 0.40C = 1.40C$

2. Selling at no profit or loss: To achieve no profit or loss, the merchant needs to sell the goods at exactly the cost price $C$.

3. Discount required: The merchant is currently charging $1.40C$ as the marked price. To sell the goods at $C$ (the cost price), he needs to offer a discount such that the selling price becomes $C$.

   $\text{Selling Price (SP)} = \text{Marked Price (MP)} - \text{Discount}$

   We want the selling price $SP$ to equal the cost price $C$, so:

   $C = 1.40C - \text{Discount}$

   Solving for the discount:

   $\text{Discount} = 1.40C - C = 0.40C$

   Therefore, the discount is 40% of the cost price. However, we need to express this as a percentage of the marked price, which is $1.40C$.

4. Percentage discount on the marked price:

   $\text{Percentage Discount} = \frac{\text{Discount}}{\text{Marked Price}} \times 100 = \frac{0.40C}{1.40C} \times 100$

   Simplifying:

   $\text{Percentage Discount} = \frac{0.40}{1.40} \times 100 \approx 28.57\%$

Thus, the approximate percentage discount is 28.5%.

The correct answer is:

(b) 28.5%

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Would you like further clarification or details? Here are 5 related questions to expand this concept:

1. What happens if the merchant offers a discount greater than 28.5%?
2. How can you calculate the new profit percentage if the merchant offers a lower discount?
3. What is the formula for calculating profit or loss percentages?
4. How does the initial markup affect the selling price in terms of profit or loss?
5. What is the impact on profit if the merchant marks up by a percentage other than 40%?

Tip: Always ensure you distinguish between percentages based on cost price and marked price, as they can lead to different interpretations of discounts or profits!