Profit & Loss

Profit & Loss

Concept Explanation

Profit and loss are the most fundamental business concepts you’ll encounter in quantitative aptitude. At its core, profit happens when you sell something for more than it cost you to acquire it. Loss is the opposite — you sold it for less than what you paid. The tricky part is that every percentage in profit and loss problems is calculated relative to the Cost Price, unless the problem explicitly says otherwise. This is where many students go wrong: they calculate profit percentage using selling price as the base, which is incorrect.

The marked price (also called list price or tag price) is what the seller initially announces. It’s the starting point before any discounts. A discount is a percentage reduction from the marked price, not from the cost price. So when you hear “20% off on a Rs. 1,000 jacket,” you’re saving Rs. 200, paying Rs. 800. But whether the seller makes a profit or loss depends entirely on what the jacket actually cost them — the discount just affects the selling price.

Overhead charges like transportation, packaging, or storage get added to the cost price. If you buy a refrigerator for Rs. 20,000 and spend Rs. 1,500 on delivery and installation, your actual cost price is Rs. 21,500. Now when you sell it, your profit or loss is calculated against Rs. 21,500, not Rs. 20,000. Always account for all costs before calculating profit percentage.

Key Formulas

Symbol	Meaning
Profit	SP − CP
Loss	CP − SP
Profit %	(Profit/CP) × 100
Loss %	(Loss/CP) × 100
SP	CP × (1 + Profit%/100)
SP	CP × (1 − Loss%/100)
Discount %	((MP − SP)/MP) × 100

Step-by-Step Example

Q: A shopkeeper buys goods at a 20% discount on the marked price of Rs. 2,500. He sells them at the marked price. What is his profit percentage?

Step 1: Find actual cost price (after 20% discount on MP): CP = 2500 × (80/100) = Rs. 2,000

Step 2: Selling price equals marked price: SP = Rs. 2,500

Step 3: Profit = SP − CP = 2500 − 2000 = Rs. 500

Step 4: Profit % = (500/2000) × 100 = 25%

Answer: 25% profit

Common Mistakes

• Calculating discount percentage on cost price instead of marked price → Discounts always apply to the marked price
• Mixing up profit percentage with markup percentage → Profit % is on CP; markup might be on MP
• Forgetting to include overhead costs in CP → Always add all acquisition costs before finding profit/loss percentage

Quick Test (2 Qs)

1. Q: A shopkeeper sells a shirt for Rs. 990 and gains 10%. What is the cost price? Options: Rs. 880, Rs. 890, Rs. 900, Rs. 910. Ans: Rs. 900 (Reason: CP = SP/(1 + 10/100) = 990/1.1 = 900)
2. Q: If the cost price of 20 articles equals the selling price of 25 articles, find the loss percentage. Options: 20%, 25%, 15%, 10%. Ans: 20% (Reason: Let CP of 1 = 1. CP of 20 = 20. SP of 25 = 20, so SP of 1 = 20/25 = 0.8. Loss% = (1 − 0.8)/1 × 100 = 20%)