If selling price is doubled, the profit triples. Find the profit percent.

### Concept & Algebraic Formulation of Profit Conditions When the relationships between changes in Selling Price (SP) and Profit (P) are given, translating these proportional changes into basic algebraic equations helps isolate the relationship between SP and Cost Price (CP). $$ \text{Profit (P)} = \text{Selling Price (SP)} - \text{Cost Price (CP)} $$ ### Step-by-Step Solution * Let the Cost Price be $C$. * Let the original Selling Price be $S$. * The original Profit is $P = S - C$. * Given: The selling price is doubled. So, New Selling Price = $2S$. * Given: The profit triples. So, New Profit = $3P$. * We know the new profit is also equal to the new selling price minus the original cost price. * Therefore, New Profit = $2S - C$. * Equate the two expressions for New Profit: $3P = 2S - C$. * Substitute the original definition of $P (S - C)$ into the equation: $3(S - C) = 2S - C$. * Expand the left side: $3S - 3C = 2S - C$. * Rearrange to solve for $S$: $3S - 2S = 3C - C \Rightarrow S = 2C$. * Now we know the original Selling Price is twice the Cost Price. * Find the original Profit Percentage: $\text{Profit } \% = (\frac{S - C}{C}) \times 100$. * Substitute $S = 2C$: $\text{Profit } \% = (\frac{2C - C}{C}) \times 100 = (\frac{C}{C}) \times 100 = 100\%$. ### Exam Strategy & Shortcut Use a test case based on options. If profit percent is $100\%$, then SP is twice the CP (e.g., CP = 10, SP = 20, Profit = 10). Double the SP: New SP = 40. New Profit = $40 - 10 = 30$. Original profit was $10$, new profit is $30$. It tripled! The condition holds perfectly. ### Common Pitfall Forgetting to substitute the initial relationship ($P = S - C$) back into the newly formed equation ($3P = 2S - C$) often leads to a dead end with too many variables and no way to isolate the ratio of $S$ to $C$. ### Final Answer Therefore, the correct answer is **100**.