A small and medium enterprise imports two components A and B from Taiwan and China respectively and assembles them with other components to form a toy. Component A contributes to 10% of production cost while component B contributes to 20% of production cost. Usually the company sells this toy at 20% above the production cost. Due to increase in the raw material and labour cost in both the countries, component A became 20% costlier and component B became 40% costlier. Owing to these reasons the company increased its selling price by 15%. Considering that cost of other components does not change, what will be the profit percentage if the toy is sold at the new price? (I.I.F.T., 2010)

### Concept & Percentage Calculation To find the new profit percentage, establish a base value for the initial total cost and calculate the incremental changes for each component and the selling price independently. $$ \text{Profit Percentage} = \left( \frac{\text{New SP} - \text{New Cost}}{\text{New Cost}} \right) \times 100 $$ ### Step-by-Step Solution * Let the initial total production cost of the toy be $100$. * Cost of Component A = $10\%$ of $100 = 10$. * Cost of Component B = $20\%$ of $100 = 20$. * Cost of other components = $100 - (10 + 20) = 70$. * Initial Selling Price (SP) = $20\%$ above cost = $120$. * New Cost of Component A = $10 + (20\% \text{ of } 10) = 12$. * New Cost of Component B = $20 + (40\% \text{ of } 20) = 28$. * Cost of other components remains unchanged at $70$. * New Total Production Cost = $12 + 28 + 70 = 110$. * New Selling Price = Initial SP increased by $15\% = 120 \times 1.15 = 138$. * New Profit = $\text{New SP} - \text{New Cost} = 138 - 110 = 28$. * New Profit Percentage = $(\frac{28}{110}) \times 100 = \frac{280}{11} \approx 25.45\%$. ### Exam Strategy & Shortcut Assume a base of $100$ to avoid fractions. The changes are straightforward: Cost goes up by $(10 \times 0.2) + (20 \times 0.4) = 2 + 8 = 10$. New cost is $110$. SP goes up by $15\%$ of $120 = 18$. New SP is $138$. Profit is $28$. $28/110$ is roughly $25.5\%$. ### Common Pitfall A common mistake is applying the $15\%$ increase to the new cost rather than the old selling price. The problem states the company increased "its selling price by 15%". ### Final Answer Therefore, the correct answer is **25.5%**.