Profit, Loss & Discount
Learning Objectives
- Understand the fundamental concepts of Profit, Loss & Discount
- Apply key formulas and techniques to solve problems
- Practice with exam-level questions to build speed and accuracy
Key Concepts
What is Profit, Loss & Discount?
Profit and loss is a core commercial arithmetic topic that deals with buying and selling goods. Questions from this topic appear regularly in SSC CGL Tier 1 and involve cost price (CP), selling price (SP), profit percentage, loss percentage, discounts, and marked price (MP).
Key Concepts
1. Basic Formulas: Profit = SP - CP (when SP > CP). Loss = CP - SP (when CP > SP). Profit% = (Profit/CP) * 100. Loss% = (Loss/CP) * 100.
2. Discount: Discount is always calculated on the Marked Price (MP). Discount% = (Discount/MP) * 100. SP = MP - Discount. Alternatively, SP = MP * (100 - d%)/100.
3. Successive Discounts: If two discounts of x% and y% are offered, single equivalent discount = x + y - (xy/100). SP = MP * (100-x)/100 * (100-y)/100.
4. False Weight / Dishonest Shopkeeper: Profit% = [(True Weight - False Weight) / False Weight] * 100. If a shopkeeper sells at cost price but uses a false weight, his profit% is the percentage of the weight difference.
Solved Examples
a) 15% b) 18% c) 20% d) 25%
a) Rs.1000 b) Rs.1020 c) Rs.1050 d) Rs.1080
a) 10% b) 11.11% c) 12.5% d) 9.09%
Shortcut Techniques
- If CP and SP are both given, profit% can be found by dividing profit by CP and multiplying by 100.
- For "if sold at Rs.x there is a loss/profit of p%" type questions, solve using CP as 100 units.
- When two items are sold at the same price, one at x% profit and one at x% loss, there is always a net loss of (x^2/100)%.
- For discount problems, use the formula: MP = SP * 100/(100 - d%) directly.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.