Step 1: Start with the cost and original margin

• Cost = $10
• Original margin = 20%

To calculate the original selling price:

Selling Price=Cost1−Margin=101−0.20=100.80=12.50\text{Selling Price} = \frac{\text{Cost}}{1 - \text{Margin}} = \frac{10}{1 - 0.20} = \frac{10}{0.80} = 12.50

Selling Price=1−MarginCost=1−0.2010=0.8010=12.50

So, the original selling price is $12.50.

Step 2: Apply a 10% discount to the selling price

Discounted Price=12.50×(1−0.10)=12.50×0.90=11.25\text{Discounted Price} = 12.50 \times (1 - 0.10) = 12.50 \times 0.90 = 11.25

Discounted Price=12.50×(1−0.10)=12.50×0.90=11.25

So, the discounted price is $11.25.

Step 3: Calculate the new margin

Margin=Selling Price−CostSelling Price=11.25−1011.25=1.2511.25≈0.1111 or 11.11%\text{Margin} = \frac{\text{Selling Price} - \text{Cost}}{\text{Selling Price}} = \frac{11.25 - 10}{11.25} = \frac{1.25}{11.25} \approx 0.1111 \text{ or } 11.11\%

Margin=Selling PriceSelling Price−Cost=11.2511.25−10=11.251.25≈0.1111 or 11.11%

✅ Final Answer:

Your new margin after giving a 10% discount is approximately 11.11%.