Define Initial and Final Conditions

Let the cost price be $C$ and the initial selling price be $S$. The initial profit is $P = S - C$. When the selling price is doubled, the new selling price is $2S$, and the profit becomes $3P$.

$P = S - C$

Set up the equation

Using the new profit condition $3P = 2S - C$, substitute $P = S - C$ into the equation.

$3(S - C) = 2S - C$

Solve for S in terms of C

Expand the equation: $3S - 3C = 2S - C$. Rearrange terms: $3S - 2S = 3C - C$, which simplifies to $S = 2C$.

$S = 2C$

Calculate Profit Percentage

The profit percentage is $\frac{S - C}{C} \times 100$. Substituting $S = 2C$: $\frac{2C - C}{C} \times 100 = \frac{C}{C} \times 100 = 100\%$.

$\text{Profit} \% = 100\%$