Language-Specific Formula Representations
Profit and Loss Formula in Hindi (लाभ और हानि सूत्र)
मूल सूत्र (Basic Formulas):
- लाभ (Profit) = विक्रय मूल्य (SP) – क्रय मूल्य (CP)
- हानि (Loss) = क्रय मूल्य (CP) – विक्रय मूल्य (SP)
- लाभ प्रतिशत = (लाभ/क्रय मूल्य) × 100
- हानि प्रतिशत = (हानि/क्रय मूल्य) × 100
- विक्रय मूल्य = क्रय मूल्य × (100 + लाभ%)/100
- अंकित मूल्य (Marked Price) = क्रय मूल्य + मार्कअप
- छूट (Discount) = अंकित मूल्य – विक्रय मूल्य
Profit and Loss Formulas in Telugu (లాభం మరియు నష్టం సూత్రాలు)
ప్రాథమిక సూత్రాలు (Basic Formulas):
- లాభం (Profit) = అమ్మకపు ధర (SP) – కొనుగోలు ధర (CP)
- నష్టం (Loss) = కొనుగోలు ధర (CP) – అమ్మకపు ధర (SP)
- లాభ శాతం = (లాభం/కొనుగోలు ధర) × 100
- నష్ట శాతం = (నష్టం/కొనుగోలు ధర) × 100
- అమ్మకపు ధర = కొనుగోలు ధర × (100 + లాభ%)/100
- తగ్గింపు (Discount) = గుర్తు ధర – అమ్మకపు ధర
Important Concepts and Tips
Main Points to Remember:
- Always Calculate Percentage on Cost Price: Profit and loss percentages are always calculated based on the cost price unless specifically mentioned otherwise.
- SP > CP → Profit: When selling price exceeds cost price, there is a profit.
- CP > SP → Loss: When cost price exceeds selling price, there is a loss.
- Discount vs. Profit: Discount is given on marked price, while profit is calculated on cost price.
- Multiple Transactions: When dealing with multiple items, calculate total CP and total SP first, then find overall profit or loss.
Common Mistakes to Avoid:
- Calculating percentage on selling price instead of cost price
- Confusing marked price with selling price
- Not converting percentage to decimal form in calculations
- Ignoring successive discounts in multi-discount scenarios
Practical Applications
Business Scenarios:
- Retail pricing strategies
- Wholesale and distribution margins
- Sale and discount planning
- Inventory management decisions
Academic Applications:
- Mathematics problem-solving
- Competitive exam preparation
- Business mathematics courses
- Financial literacy education
Frequently Asked Questions about Profit and Loss Formulas
Q. What is the basic formula for profit and loss?
The basic formulas are:
- Profit = Selling Price (SP) – Cost Price (CP), when SP > CP
- Loss = Cost Price (CP) – Selling Price (SP), when CP > SP
These fundamental formulas form the basis of all profit and loss calculations. The cost price is what you pay to acquire an item, and the selling price is what you receive when selling it.
Q. How do you calculate profit percentage and loss percentage?
- Profit Percentage = (Profit/Cost Price) × 100
- Loss Percentage = (Loss/Cost Price) × 100
Important Note: Profit and loss percentages are always calculated on the Cost Price (CP) unless the question specifically states otherwise. For example, if CP = ₹500 and SP = ₹600, Profit = ₹100, and Profit % = (100/500) × 100 = 20%.
Q. What is the difference between marked price and selling price?
- Marked Price (MP): The price tag displayed on a product; the initial price before any discount.
- Selling Price (SP): The actual price at which the product is sold to the customer after applying any discounts.
Formula: SP = MP – Discount, or SP = MP × (100 – Discount%)/100
For example, if a shirt has MP = ₹1000 and a 20% discount is offered, then SP = 1000 × (80/100) = ₹800.
Q. How do you find the cost price when selling price and profit percentage are given?
Use the formula: CP = SP × 100/(100 + Profit%)
Example: If an item is sold for ₹1200 at a 20% profit: CP = 1200 × 100/(100 + 20) = 1200 × 100/120 = ₹1000
Similarly, for loss: CP = SP × 100/(100 – Loss%)
Q. What is the formula for successive discounts?
When two discounts d₁% and d₂% are applied successively:
Single Equivalent Discount = [d₁ + d₂ – (d₁ × d₂)/100]%
Example: If 20% and 10% discounts are applied: Equivalent Discount = [20 + 10 – (20 × 10)/100] = [30 – 2] = 28%
Note: Two successive discounts of 20% and 10% are NOT equal to a single 30% discount.
Q. If an item is sold at a 10% loss, what should be the selling price to gain 10% profit?
This requires finding the cost price first, then calculating the new selling price.
Step 1: If SP₁ = 100 (assuming), and there’s 10% loss: CP = SP₁ × 100/(100 – 10) = 100 × 100/90 = ₹111.11 (approx.)
Step 2: For 10% profit: SP₂ = CP × (100 + 10)/100 = 111.11 × 110/100 = ₹122.22
- Percentage increase = [(122.22 – 100)/100] × 100 = 22.22%
- Formula: Percentage change = [(P₁ + P₂ + P₁×P₂/100)]%, where P₁ = -10 (loss) and P₂ = 10 (profit)
Q. How do you calculate overall profit or loss when multiple items are bought and sold?
Calculate the total cost price and total selling price for all items, then find the difference.
Overall Profit/Loss = Total SP – Total CP
Example:
- Item A: CP = ₹500, SP = ₹600 (Profit = ₹100)
- Item B: CP = ₹300, SP = ₹250 (Loss = ₹50)
Total CP = ₹800, Total SP = ₹850 Overall Profit = ₹850 – ₹800 = ₹50 Overall Profit % = (50/800) × 100 = 6.25%
Q. What is the relationship between discount, marked price, and profit?
The relationship involves three prices:
CP → MP → SP
- Markup is added to CP to get MP
- Discount is subtracted from MP to get SP
- Profit = SP – CP
Example: If CP = ₹800, Markup = 25%, Discount = 10%:
- MP = 800 × 125/100 = ₹1000
- SP = 1000 × 90/100 = ₹900
- Profit = 900 – 800 = ₹100 (12.5% profit)
Q. How do you solve problems involving false weights or measures?
When a dishonest trader uses false weights, the formula is:
Profit % = [(True Weight – False Weight)/False Weight] × 100
Example: A shopkeeper claims to sell at cost price but uses a 900g weight instead of 1kg (1000g): Profit % = [(1000 – 900)/900] × 100 = (100/900) × 100 = 11.11%
Note: This is a theoretical scenario for educational purposes; honest trading practices should always be followed.
Q. What are some quick tricks for solving profit and loss problems in competitive exams?
Here are proven time-saving techniques:
1. 10% Rule: For 10% profit, SP = 1.1 × CP; for 10% loss, SP = 0.9 × CP
2. Doubling/Halving: 100% profit means SP = 2 × CP; 50% loss means SP = 0.5 × CP
3. Alligation Method: For finding the ratio in which items at different prices should be mixed
4. Percentage Change: Loss% + Profit% = Net Profit% + (Loss% × Profit%)/100
5. Break-even Analysis: If selling n items at a loss, calculate how many must be sold at profit to break even
6. Unitary Method: First find the value for one unit, then calculate for the required quantity
7. Approximation: In MCQ exams, approximate calculations can save time significantly
Study Tips:
- Practice problems daily with different variations
- Create flashcards for quick formula recall
- Solve previous year exam questions
- Apply formulas to real-life shopping scenarios
- Use mental math for common percentages (10%, 20%, 25%, 50%)
