Understand the Given Condition

We are given that the cost price of 15 pens is equal to the selling price of 10 pens. Let us write this as an equation: $15 \times CP = 10 \times SP$.

$15 \times CP = 10 \times SP$

Find the Ratio of SP to CP

Rearranging the equation to find the ratio of selling price to cost price: $\frac{SP}{CP} = \frac{15}{10} = \frac{3}{2} = 1.5$.

$\frac{SP}{CP} = \frac{3}{2}$

Calculate the Profit Percentage

Using the formula for profit percentage: $\text{Profit} \% = \left(\frac{SP - CP}{CP}\right) \times 100 = \left(\frac{3 - 2}{2}\right) \times 100 = \frac{1}{2} \times 100 = 50\%$.

$\text{Profit} \% = 50\%$