If the gross profit margin was 12% on a smartphone, find the mark up on the cost.

To find the markup on the cost given the gross profit margin, we need to relate the gross profit margin to the markup percentage. Here's how we can do that:

1. **Gross Profit Margin Formula**:
   \[
   \text{Gross Profit Margin} = \frac{\text{Selling Price} - \text{Cost}}{\text{Selling Price}} \times 100
   \]
   We're given that the gross profit margin is 12%, so:
   \[
   12 = \frac{\text{Selling Price} - \text{Cost}}{\text{Selling Price}} \times 100
   \]
   This simplifies to:
   \[
   \frac{\text{Selling Price} - \text{Cost}}{\text{Selling Price}} = 0.12
   \]
   Therefore, the cost is 88% (or $1 - 0.12 = 0.88$) of the selling price.

2. **Markup on Cost Formula**:
   The markup is given by:
   \[
   \text{Markup} = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100
   \]
   Let’s express the selling price in terms of the cost. From step 1, we know that:
   \[
   \text{Cost} = 0.88 \times \text{Selling Price}
   \]
   So, $\text{Selling Price} = \frac{\text{Cost}}{0.88}$.

3. **Substitute into Markup Formula**:
   Now, substitute into the markup formula:
   \[
   \text{Markup} = \frac{\frac{\text{Cost}}{0.88} - \text{Cost}}{\text{Cost}} \times 100
   \]
   Simplifying this expression:
   \[
   \text{Markup} = \frac{\text{Cost}(1 - 0.88)}{0.88 \times \text{Cost}} \times 100
   \]
   \[
   \text{Markup} = \frac{0.12}{0.88} \times 100
   \]
   \[
   \text{Markup} \approx 13.64\%
   \]

Thus, the markup on the cost is approximately **13.64%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the difference between markup and gross profit margin?
2. How do we calculate markup if both cost and selling price are known?
3. If the cost was $100, what would be the selling price given a markup of 13.64%?
4. How would the gross profit margin change with a higher markup?
5. Can markup ever be negative?

**Tip:** Markup is based on the cost, while the gross profit margin is based on the selling price. These percentages give different perspectives on profitability.

If the gross profit margin was 12% on a smartphone, find the markup on the cost.

Understand how to calculate the markup on cost when given a gross profit margin of 12% for a smartphone. This problem involves key concepts like profit margin and percentage calculations, making it ideal for students in Grades 9-11.

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