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: Assume a total number of articles and a cost price per article. Let the total number of articles be 8 (to simplify calculations with the fraction (5)/(8)). Let the cost price (CP) of each article be ₹100. The total cost price for all 8 articles is 8 × ₹100 = ₹800. Step 2: Calculate the selling price for the first part of the articles. The shopkeeper sold (5)/(8) of his articles at a gain of 20\%. Number of articles in this part = (5)/(8) × 8 = 5 articles. Cost price of these 5 articles = 5 × ₹100 = ₹500. Selling price (SP) of these 5 articles = CP × (1 + Gain Percentage) SP_1 = ₹500 × (1 + (20)/(100)) = ₹500 × 1.20 = ₹600. Step 3: Calculate the selling price for the remaining articles. Remaining articles = Total articles - Articles in the first part = 8 - 5 = 3 articles. These remaining articles were sold at the cost price. Cost price of these 3 articles = 3 × ₹100 = ₹300. Selling price of these 3 articles = CP = ₹300. SP_2 = ₹300. Step 4: Calculate the total selling price and total gain. Total selling price = SP_1 + SP_2 = ₹600 + ₹300 = ₹900. Total cost price = ₹800. Total gain = Total selling price - Total cost price = ₹900 - ₹800 = ₹100. Step 5: Calculate the overall gain percentage. Gain percentage = Total GainTotal Cost Price × 100\% Gain Percentage = ₹100₹800 × 100\% Gain Percentage = (1)/(8) × 100\% Gain Percentage = 12.5\% As a mixed fraction, 12.5\% is 12(1)/(2)\%. The final answer is 12(1)/(2)\%. Send me the next one 📸