This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the given relationship between selling price (SP) and cost price (CP). The question states that the selling price of 15 articles is equal to the cost price of 20 articles. Let SP be the selling price of one article and CP be the cost price of one article. According to the problem: 15 × SP = 20 × CP Step 2: Find the ratio of SP to CP. Divide both sides by 15 × CP: (SP)/(CP) = (20)/(15) Simplify the fraction: (SP)/(CP) = (4)/(3) This implies that SP = (4)/(3) CP. Step 3: Determine if there is a profit or loss. Since SP = (4)/(3) CP, and (4)/(3) > 1, it means SP > CP. Therefore, there is a profit. Step 4: Calculate the profit. Profit = SP - CP Substitute the expression for SP: Profit = (4)/(3) CP - CP Profit = ((4)/(3) - 1) CP Profit = ((4-3)/(3)) CP Profit = (1)/(3) CP Step 5: Calculate the profit percentage. The formula for profit percentage is: Profit Percentage = (Profit)/(CP) × 100\% Substitute the calculated profit: Profit Percentage = (1)/(3) CPCP × 100\% Profit Percentage = (1)/(3) × 100\% Profit Percentage = (100)/(3)\% Profit Percentage = 33(1)/(3)\% The overall profit percentage is 33(1)/(3)\%. The final answer is 33(1)/(3)\% profit.