 If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at the cost price, what was the mark up percentage?  use assumption method

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%**.

---

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.

If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at the cost price, what was the mark up percentage? Use assumption method.

Learn how to calculate the markup percentage when a merchant offers a 40% discount and sells at cost price. This detailed step-by-step solution covers key mathematical concepts like percentage, markup, and discount. Suitable for students in Grades 8-10.

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