Set up the equation

Equate the given cost price and selling price conditions: $10 imes \text{CP} = 8 imes \text{SP}$.

$10 imes \text{CP} = 8 imes \text{SP}$

Find the ratio of SP to CP

Rearranging the equation gives the ratio of selling price to cost price: $\frac{\text{SP}}{\text{CP}} = \frac{10}{8} = \frac{5}{4}$.

$rac{\text{SP}}{\text{CP}} = \frac{5}{4}$

Calculate profit percentage

Using the profit percentage formula with $\text{CP} = 4$ and $\text{SP} = 5$: $\text{Profit } \% = \frac{5 - 4}{4} imes 100 = 25\%.$

$ext{\text{Profit} } \% = \frac{1}{4} imes 100 = 25\%$