Profit and Loss Explained: Formulas, Examples, and Easy Tricks - Aptitude Questions & Answers
Profit and Loss Explained: Formulas, Examples, and Easy Tricks is one of the most important topics in Quantitative Aptitude. In this lesson, you will learn concepts, formulas, shortcuts, solved examples, and aptitude questions with answers. This topic is useful for exams like SSC, Bank, CAT, TCS, and other competitive exams.
Profit and Loss: Complete Guide with Formulas & Examples
Basic Concepts in Profit and Loss
Profit and Loss is a fundamental business mathematics concept that helps determine financial outcomes of buying and selling transactions. Understanding these concepts is crucial for business owners, traders, and competitive exam aspirants.
Essential Terms and Formulas
Cost Price (CP)
The amount a seller pays to purchase a product or commodity. This includes the purchase price plus any additional expenses incurred.
Example: A shopkeeper buys a watch for ₹2,000. This ₹2,000 is the Cost Price.
Selling Price (SP)
The amount at which a product is sold to the customer. This is the price the buyer pays for the item.
Example: The same watch is sold to a customer for ₹2,500. This ₹2,500 is the Selling Price.
Key Difference: CP is what the seller pays, SP is what the buyer pays.
Profit
The financial gain obtained when Selling Price exceeds Cost Price.
P = SP - CP
Example Problem: A shopkeeper buys apples for ₹400/kg and sells them for ₹550/kg.
CP = ₹400, SP = ₹550
Profit = ₹550 - ₹400 = ₹150 per kg
Loss
The financial loss incurred when Selling Price is less than Cost Price.
L = CP - SP
Example Problem: John bought a bicycle for ₹5,000 and sold it for ₹4,000.
CP = ₹5,000, SP = ₹4,000
Loss = ₹5,000 - ₹4,000 = ₹1,000
Percentage Calculations in Profit and Loss
Profit Percentage
Profit percentage measures profit relative to the Cost Price, expressed as a percentage.
OR
Profit % = (Profit / CP) × 100
Example Problem: Emma buys a necklace for ₹12,000 and sells it for ₹18,000.
- CP = ₹12,000, SP = ₹18,000
- Profit = ₹18,000 - ₹12,000 = ₹6,000
- Profit % = (6,000 / 12,000) × 100 = 50%
Quick Calculation Method: When SP and CP are known
Profit % = [(SP/CP - 1)] × 100
In above example: (18,000/12,000 - 1) × 100 = (1.5 - 1) × 100 = 50%
Loss Percentage
Loss percentage measures loss relative to the Cost Price, expressed as a percentage.
OR
Loss % = (Loss / CP) × 100
Example Problem: Mike buys a smartphone for ₹15,000 and sells it for ₹12,000.
- CP = ₹15,000, SP = ₹12,000
- Loss = ₹15,000 - ₹12,000 = ₹3,000
- Loss % = (3,000 / 15,000) × 100 = 20%
Important Derived Formulas
Finding SP when CP and Profit % are known
Example: CP = ₹800, Profit% = 25%
SP = 800 × [(100 + 25)/100] = 800 × 1.25 = ₹1,000
Finding SP when CP and Loss % are known
Example: CP = ₹800, Loss% = 15%
SP = 800 × [(100 - 15)/100] = 800 × 0.85 = ₹680
Finding CP when SP and Profit % are known
Example: SP = ₹1,200, Profit% = 20%
CP = 1,200 × [100/(100 + 20)] = 1,200 × (100/120) = ₹1,000
Finding CP when SP and Loss % are known
Example: SP = ₹850, Loss% = 15%
CP = 850 × [100/(100 - 15)] = 850 × (100/85) = ₹1,000
Marked Price, Discount, and Discount Percentage
Marked Price (MP)
The price displayed on the product tag before any discount is applied. Shopkeepers mark products at a higher price to offer discounts and attract customers.
Example: A shirt with a price tag showing ₹1,200 has a Marked Price of ₹1,200.
Discount
The reduction in price offered to customers from the Marked Price.
D = MP - SP
Example Problem: A book marked at ₹300 is sold for ₹275.
MP = ₹300, SP = ₹275
Discount = ₹300 - ₹275 = ₹25
Discount Percentage
The percentage reduction from the Marked Price.
OR
Discount % = [(MP - SP) / MP] × 100
Example Problem: A bag marked at ₹1,000 is sold for ₹800.
- MP = ₹1,000, SP = ₹800
- Discount = ₹1,000 - ₹800 = ₹200
- Discount % = (200 / 1,000) × 100 = 20%
Relationship Between MP, CP, and Discount
Profit = SP - CP
SP = MP - Discount
∴ Profit = (MP - Discount) - CP
Example: A product with CP = ₹500 is marked at ₹700 and sold at 10% discount.
- MP = ₹700
- Discount = 10% of ₹700 = ₹70
- SP = ₹700 - ₹70 = ₹630
- Profit = ₹630 - ₹500 = ₹130
- Profit % = (130/500) × 100 = 26%
Types of Discounts in Market
1. \"Up To\" Discount
A marketing strategy where maximum discount percentage is advertised, but actual discounts vary across products.
Example: \"Up to 50% off\" sale means:
- Some items might have 50% discount
- Others might have 30%, 20%, or 10% discount
- The advertised percentage is the maximum, not the uniform discount
Purpose: Attracts customers with headline discount while maintaining profitability on most items.
2. Flat Discount
A uniform percentage or amount reduction applied to all eligible products.
Example: \"Flat 30% off on all electronics\" means:
- Every electronic item gets exactly 30% discount
- No variation in discount percentage
- Easy to calculate final price
Calculation: If MP = ₹2,000, then SP = ₹2,000 × 0.70 = ₹1,400
3. Successive Discounts
Multiple discounts applied one after another on the same product. This creates a compounded discount effect.
Two Successive Discounts Formula
Effective Discount % = x + y - (x × y / 100)
Note: This formula works only for two successive discounts.
Example Problem: Calculate effective discount for successive discounts of 40% and 50%.
- First discount: 40%
- Second discount: 50%
- Effective Discount % = 40 + 50 - (40 × 50 / 100)
- Effective Discount % = 90 - 20 = 70%
Step-by-Step Calculation: MP = ₹1,000 with 40% and 50% discounts
- After 40% discount: Price = ₹1,000 - 40% of ₹1,000 = ₹600
- After 50% discount on ₹600: Price = ₹600 - 50% of ₹600 = ₹300
- Total discount = ₹1,000 - ₹300 = ₹700
- Discount % = (700/1,000) × 100 = 70% ✓
Three Successive Discounts Method
For three discounts x%, y%, and z%, calculate step by step:
- Apply first discount to MP
- Apply second discount to result
- Apply third discount to that result
- Calculate overall discount percentage
Example: MP = ₹2,000 with discounts of 20%, 10%, and 5%
After 20%: ₹1,600 → After 10%: ₹1,440 → After 5%: ₹1,368
Total discount = ₹632, Discount % = 31.6%
Special Case: When SP is Same After Profit and Loss
Profit of P% on one transaction
Loss of L% on another transaction
Then, Loss % = (P × L) / 100
Example: A man sells two watches for ₹2,400 each. On one he gains 20%, on other he loses 20%.
Overall Loss % = (20 × 20) / 100 = 4%
Verification: Total CP = ₹5,000, Total SP = ₹4,800, Loss = ₹200, Loss % = 4%
Profit and Loss: Frequently Asked Questions
What is the difference between Cost Price and Selling Price?
Cost Price is what the seller pays to acquire the product. Selling Price is what the customer pays to purchase it. Profit occurs when SP > CP, Loss occurs when SP < CP.
How to calculate profit percentage when both CP and SP are known?
Use formula: Profit % = [(SP - CP) / CP] × 100. For example, CP = ₹800, SP = ₹1,000 gives Profit % = [(200)/800] × 100 = 25%.
Why are successive discounts less than the sum of individual discounts?
Because each discount is applied on the reduced price from previous discount, not on original price. This compounding effect makes total discount less than simple addition of percentages.
What is marked price and why is it important?
Marked Price is the price displayed before discount. It\'s important for discount calculations and creates psychological appeal for customers who feel they\'re getting a deal when buying at discounted price.
How to find Cost Price when Selling Price and Profit % are given?
Use formula: CP = SP × [100 / (100 + Profit%)]. For example, SP = ₹1,200 with 20% profit gives CP = 1,200 × (100/120) = ₹1,000.
Practice Problems
Problem 1
A shopkeeper buys 80 articles for ₹2,400 and sells them for a profit of 16%. Find the selling price of one article.
Problem 2
A product is marked at ₹1,500. After two successive discounts of 20% and 10%, what is the selling price?
Problem 3
By selling 45 oranges for ₹160, a woman loses 20%. How many oranges should she sell for ₹112 to gain 20%?
Frequently Asked Questions
What is Profit and Loss Explained: Formulas, Examples, and Easy Tricks?
Profit and Loss Explained: Formulas, Examples, and Easy Tricks is an important aptitude topic used in competitive exams that tests your logical reasoning and problem-solving abilities.
Is Profit and Loss Explained: Formulas, Examples, and Easy Tricks important for competitive exams?
Yes, Profit and Loss Explained: Formulas, Examples, and Easy Tricks is frequently asked in SSC, Bank, CAT, TCS, and other placement exams. It's essential to master this topic for better scores.
How to prepare Profit and Loss Explained: Formulas, Examples, and Easy Tricks easily?
Practice solved examples, learn formulas and shortcuts, and attempt practice questions regularly to master Profit and Loss Explained: Formulas, Examples, and Easy Tricks.
What are the important formulas in Profit and Loss Explained: Formulas, Examples, and Easy Tricks?
Key formulas vary by topic, but generally include basic concepts, shortcuts, and standard problem-solving approaches specific to Profit and Loss Explained: Formulas, Examples, and Easy Tricks.
How many questions come from Profit and Loss Explained: Formulas, Examples, and Easy Tricks?
Typically 5-10 questions come from Profit and Loss Explained: Formulas, Examples, and Easy Tricks in most competitive exams, making it a high-scoring section.
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