One-Line Definition
Profit & Loss analyzes financial transactions involving Cost Price (CP), Selling Price (SP), and Marked Price (MP). Profit occurs when SP > CP, Loss occurs when SP < CP, and Discount is calculated on MP.
Storeowner Mental Model
Follow the pricing chain step-by-step:
- 1. Buy item for ₹1,000 (Cost Price - CP)
- 2. Tag price tag as ₹1,500 (Marked Price - MP) [50% Markup]
- 3. Give customer 20% Discount (₹300)
- 4. Final Price = ₹1,200 (Selling Price - SP) → Profit = ₹200 (20%)
Profit, Loss & Discount is one of the highest-weightage topics in entrance exams like CAT, NMAT, SNAP, and MBA CET. Questions test both pure calculation and multi-step business logic:
Example:
A merchant buys a shirt for ₹800 and sells it for ₹1,000.
Profit = ₹1,000 - ₹800 = ₹200. Profit % = (200 / 800) × 100 = 25%.
Thinking in Multipliers (Shortcut)
SHORTCUT RULES & KEY FORMULAS
Dishonest Dealer Faulty Weight
Used when a trader claims to sell goods at cost price but uses false lighter weights.
Selling 2 Items at Same SP
When two items are sold at the exact same Selling Price, one at a profit of x% and the other at a loss of x%.
SOLVED EXAMPLES (LEVEL 0 TO HARD)
Q: A shopkeeper buys a bag for ₹800 and sells it for ₹1,000. Find the profit percentage.
Step 1: Profit = SP - CP = 1000 - 800 = ₹200.
Step 2: Profit % = (Profit / CP) × 100 = (200 / 800) × 100 = 25%.
Q: A trader marks an item 25% above Cost Price and offers a 10% discount. Find the net profit percentage.
Step 1: Assume CP = ₹100.
Step 2: Marked Price (MP) = 100 × 1.25 = ₹125.
Step 3: Discount = 10% of 125 = ₹12.50 → SP = 125 - 12.50 = ₹112.50.
Step 4: Profit = 112.50 - 100 = 12.50% net profit.
Q: A dishonest dealer professes to sell his goods at cost price, but uses an 800g weight for a 1kg weight. Find his profit percentage.
Step 1: True Weight = 1000g. False Weight = 800g. Error = 1000 - 800 = 200g.
Step 2: Profit % = [ Error / (True Weight - Error) ] × 100.
Step 3: Profit % = (200 / 800) × 100 = 25%.
Mistake 1
Calculating Profit on SP
Calculating profit percentage using Selling Price (SP) instead of Cost Price (CP). Profit is ALWAYS (Profit / CP) × 100 unless stated as margin on SP.
Mistake 2
Subtracting Percentages Directly
A 50% markup followed by a 20% discount does NOT equal 30% profit. Always multiply Factors: 1.50 × 0.80 = 1.20 (which is 20% profit).
Mistake 3
Assuming No Loss on Same SP
Selling two items at the same price (+20% and -20%) does NOT balance out to 0%. It ALWAYS yields a net loss of (x/10)² = 4%.
1. An item bought for ₹500 is sold at a profit of 15%. Find its Selling Price.
Answer: SP = 500 × 1.15 = ₹575.
2. An article marked ₹1,200 is sold after two successive discounts of 20% and 10%. Find the final Selling Price.
Answer: SP = 1200 × 0.80 × 0.90 = 1200 × 0.72 = ₹864.
3. A shopkeeper marks his goods 40% above CP and allows a 25% discount. If he also uses a false weight of 900g for 1kg, find his overall profit percentage.
Answer: Multiplier = 1.40 × 0.75 × (1000/900) = 1.05 × 1.111 = 1.1667 → Overall Profit = 16.67%.
FREQUENTLY ASKED QUESTIONS
❓ Why is Profit % always calculated on Cost Price (CP)?
Cost Price represents your initial capital investment. Calculating profit percentage on CP reflects the true return on investment (ROI). Unless explicitly mentioned as 'profit on selling price', always use CP as the denominator.
❓ How do you quickly solve Dishonest Dealer faulty weight questions?
Use the formula Profit % = [ Error / (True Weight - Error) ] × 100. For example, if a dealer gives 900g instead of 1000g, the error is 100g, so Profit % = (100 / 900) × 100 = 11.11%.
❓ What happens when two items are sold at the same selling price with identical profit and loss percentages?
When two articles are sold at the same Selling Price, one at a profit of x% and the other at a loss of x%, the transaction ALWAYS results in an overall net loss given by (x / 10)² %.