Vedanta_Class8_Math_Unit7_Formulas

Unit 7: Profit, Loss, and Discount — Cheat Sheet & Practice Guide This reference companion maps out the foundational formulas and step-by-step methods used in your Class 8 Mathematics textbook to solve problems involving Marked Price (MP), Selling Price (SP), Cost Price (CP), and Discounts. 1. The Core Formula Vault • Discount Amount = Marked Price (MP) - Selling Price (SP) • Selling Price (SP) = Marked Price (MP) - Discount Amount • Marked Price (MP) = Selling Price (SP) + Discount Amount • Discount Percentage (Discount %) = (Discount Amount / MP) * 100% • Discount Amount = (Discount % / 100) * MP • SP when given MP & Discount %: SP = MP * (1 - Discount%/100) = [MP * (100 - Discount%)] / 100 • MP when given SP & Discount %: MP = (SP * 100) / (100 - Discount%) 2. Worked Problem Archetypes (Step-by-Step) Archetype A: Finding MP when SP and Discount % are given Problem: A jacket is sold for Rs. 1,530 after allowing a 15% discount. Find its Marked Price. Step 1: Identify given values. Here, Selling Price (SP) = Rs. 1,530, and Discount % = 15%. Step 2: Use the direct MP formula: MP = (SP * 100) / (100 - Discount%) Step 3: Substitute values: MP = (1530 * 100) / (100 - 15) MP = 153000 / 85 Step 4: Calculate the final division: MP = Rs. 1,800 Archetype B: Finding Discount % from MP and SP Problem: A textbook has a marked price of Rs. 500 but is sold to a student for Rs. 425. Calculate the discount percentage allowed. Step 1: Identify given values. MP = Rs. 500, SP = Rs. 425. Step 2: Find the absolute Discount Amount: Discount Amount = MP - SP = 500 - 425 = Rs. 75. Step 3: Apply the Discount % formula: Discount % = (Discount Amount / MP) * 100% Discount % = (75 / 500) * 100% Step 4: Simplify: Discount % = 75 / 5 = 15%