Explanation:

- When a mobile phone is sold at a profit of 80%, the selling price is 180% of the cost price.

- To find the profit as a percentage of the selling price, use the formula: $$\text{Profit percentage of selling price}=\left(\frac{\text{Profit}}{\text{Selling Price}}\right)\times 100\mathrm{\%}$$

- Let the cost price be $100$ units. The profit is then $80$ units (since 80% of 100).

- The selling price is $180$ units (100 units cost price + 80 units profit).

- Plugging these values into the formula: $$\left(\frac{80}{180}\right)\times 100\mathrm{\%}=44.44\mathrm{\%}$$

- Correct Answer: Option 3: 44.44%