The ratio of cost price to sale price is $20:23$. What is the profit percentage?

Let the cost price ($\text{CP}$) be $20x$ and the sale price ($\text{SP}$) be $23x$.
The profit made is given by:

$$\text{Profit}=\text{SP}-\text{CP}=23x-20x=3x$$

The profit percentage is calculated with respect to the cost price:

$$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100\%=\left(\frac{3x}{20x}\right)\times 100\%=3\times 5\%=15\%$$