Profit and Loss
Pointwise AISSEE Class 6 Mathematics guide for Profit and Loss (Topic 6). Master cost price, selling price, overheads, profit %, loss %, and rapid commercial transaction calculations.
Overview & Fundamental Concept
Pointwise AISSEE Class 6 Mathematics guide for Profit and Loss (Topic 6). Master cost price, selling price, overheads, profit %, loss %, and rapid commercial transaction calculations.
Official Syllabus Coverage Breakdown
| Syllabus Item | Prescribed Scope | Exam Relevance & Pedagogical Objective |
|---|---|---|
| Item 6 | Cost price (CP), selling price (SP), profit and loss, overhead expenses, profit percentage, loss percentage on cost price. | Master CP, SP, overhead accumulation, profit and loss percentages calculated strictly on CP, and commercial arithmetic word problems for AISSEE Class VI. |
1. Commercial Foundations: Cost Price, Selling Price & Overheads
- Cost Price (CP): The total amount paid to acquire an article, including purchase price plus all additional overhead expenses.
- Selling Price (SP): The price at which an article is sold to a customer or buyer.
- Overhead Expenses (Overhead Charges): Additional expenses incurred after purchasing an article, such as transportation, packing, labor, repairs, or octroi. Overhead expenses are ALWAYS added directly to the purchase price to obtain the Effective Cost Price: $$\text{Effective CP} = \text{Purchase Price} + \text{Overhead Expenses}$$
- Break-Even Condition: When $\text{SP} = \text{CP}$, there is neither profit nor loss.
| Commercial Term | Abbreviation | Definition | Example Calculation |
|---|---|---|---|
| Cost Price | CP | Total expenditure to purchase/prepare goods | Bought bicycle for ₹2,400 |
| Overhead Expenses | Overheads | Repairs, transit, taxes added to purchase | Spent ₹200 on new tyres and ₹100 on painting |
| Effective Cost Price | Total CP | Purchase Price + Overheads | ₹2,400 + ₹200 + ₹100 = ₹2,700 |
| Selling Price | SP | Amount received on sale | Sold bicycle for ₹3,240 |
| Profit | Gain | Surplus when SP > CP | ₹3,240 − ₹2,700 = ₹540 |
2. Profit vs. Loss Conditions & Percentage Calculations
- Condition for Profit (Gain): When Selling Price is greater than Cost Price ($\text{SP} > \text{CP}$): $$\text{Profit} = \text{SP} - \text{CP}$$
- Condition for Loss: When Cost Price is greater than Selling Price ($\text{CP} > \text{SP}$): $$\text{Loss} = \text{CP} - \text{SP}$$
- The Cardinal Rule of Percentage: Profit percentage and Loss percentage are ALWAYS calculated strictly on the Cost Price (CP), never on the Selling Price: $$\text{Profit }\% = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100$$ $$\text{Loss }\% = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100$$
- Finding SP from CP:
• In case of Profit: $\text{SP} = \text{CP} \times \left(\frac{100 + P\%}{100}\right)$
• In case of Loss: $\text{SP} = \text{CP} \times \left(\frac{100 - L\%}{100}\right)$ - Finding CP from SP:
• In case of Profit: $\text{CP} = \frac{\text{SP} \times 100}{100 + P\%}$
• In case of Loss: $\text{CP} = \frac{\text{SP} \times 100}{100 - L\%}$
Cadet Mnemonic • P-O-C Memory Rule
Never calculate on SP:
- Percentage is
- Over
- Cost Price (Denominator = CP)
AISSEE Trap Alert • The Selling Price Denominator Trap
Candidates often accidentally divide profit by SP. Remember: Profit% = (Profit / CP) × 100. If an item bought for ₹80 is sold for ₹100, Profit = ₹20. Profit% = (20 / 80) × 100 = 25%, NOT (20 / 100) × 100 = 20%!
3. Advanced Commercial Models & Multiplier Shortcuts
- Decimal Multiplier Method:
• For $20\%$ profit: $\text{SP} = 1.20 \times \text{CP}$
• For $15\%$ loss: $\text{SP} = 0.85 \times \text{CP}$
• For $50\%$ profit: $\text{SP} = 1.50 \times \text{CP}$ - Articles Sold = Cost of Articles Model: If the cost price of $m$ articles equals the selling price of $n$ articles ($m \cdot \text{CP} = n \cdot \text{SP}$): $$\text{Profit/Loss }\% = \left(\frac{m - n}{n}\right) \times 100$$ If positive, it is a profit; if negative, a loss.
- Equal SP with Identical P% and L% Trap: If two items are sold at the same SP, one at $x\%$ profit and the other at $x\%$ loss, there is ALWAYS an overall net loss of: $$\text{Net Loss }\% = \left(\frac{x}{10}\right)^2 = \frac{x^2}{100}\%$$
Exam Trick • Same SP Twin Transaction Rule
When two articles sell at the same price, one at 20% profit and one at 20% loss: Net Loss% = (20 / 10)² = 2² = 4% loss! Never mark 'No profit no loss'.
Visual Concept Blueprint • Vector Architecture
Speed Shortcuts & Mental Calculation Strategies
Master these high-yield time-saving heuristics curated by top AISSEE scorers to eliminate calculation bottlenecks and answer questions in under 45 seconds.
Shortcut Technique 1: Effective CP Accumulator
Always sum up all incidental costs (transport, repair, paint) into the initial buying price before applying any profit/loss formula.
Shortcut Technique 2: Unit SP vs Total SP Choice
If transaction involves dozens or cartons, find profit/loss per single article to avoid massive multi-digit arithmetic.
Shortcut Technique 3: Fractional Multiplier Shortcut
25% profit means SP is 5/4 of CP. 20% loss means SP is 4/5 of CP. Multiply or divide directly by these fractions.
Interactive 3D Revision Flashcards Deck
Click any card to flip and reveal the key exam rule or topper secret.
REVISION FLASHCARD
What is the core rule & definition for Profit and Loss?
CADET MEMORY KEY
Profit: \text{Profit} = \text{SP} - \text{CP} \quad (\text{when } \text{SP} > \text{CP})
REVISION FLASHCARD
Cadet Shortcut: How to solve Profit and Loss in under 30 seconds?
CADET MEMORY KEY
Fast MCQ Elimination: Check the last digit (unit digit) and estimate the order of magnitude to eliminate 2 distractors in under 10 seconds.
REVISION FLASHCARD
Exam Trap Alert: What pitfall do most candidates fall into?
CADET MEMORY KEY
Overhead Expenses: Transportation, repairs, or labor must be ADDED to buying price to get Real CP.
REVISION FLASHCARD
Rapid Memory Anchor for AISSEE Hall Recall:
CADET MEMORY KEY
Base of Percentage: Profit % and Loss % are ALWAYS calculated on Cost Price (CP).
REVISION FLASHCARD
If the cost price of 10 pens equals the selling price of 8 pens, find the profit percentage.
CADET MEMORY KEY
Profit% = [(10 − 8) / 8] × 100 = (2 / 8) × 100 = 25% profit.
Common Traps & Examination Pitfalls
Avoid the Speed-Guess Trap: Under AISSEE pressure, candidates frequently misread units (e.g., mixing metres and centimetres, or per hour and per second) and confuse complementary ($90^\circ$) with supplementary ($180^\circ$) angles. Read every stem carefully and check units before selecting your OMR option.
Key Identities & Formulas
Profit Percentage
$$\text{Profit}\% = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100$$
Strictly computed over Cost Price.
Loss Percentage
$$\text{Loss}\% = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100$$
Strictly computed over Cost Price.
Selling Price Formula
$$\text{SP} = \text{CP} \times \frac{100 \pm \%}{100}$$
Use + for profit %, - for loss %.
Step-by-Step Solved Examination Models
Solved Example 1
Model Problem
A trader buys a table for ₹250 and sells it for ₹300. Calculate his profit percentage.
Detailed Solution:
CP = ₹250, SP = ₹300. Profit = 300 − 250 = ₹50. Profit % = (Profit / CP) × 100 = (50 / 250) × 100 = 20%.
Solved Example 2
Model Problem
A bicycle bought for ₹1,800 was sold at a loss of 15%. What was its selling price?
Detailed Solution:
Loss = 15% of 1,800 = (15 / 100) × 1,800 = ₹270. SP = CP − Loss = 1,800 − 270 = ₹1,530.
Solved Example 3
Model Problem
A merchant bought an old refrigerator for ₹4,500 and spent ₹500 on its repair and transportation. He then sold it for ₹6,000. Find his profit or loss percentage.
Detailed Solution:
1. Purchase Price = ₹4,500; Overheads = ₹500.
2. $\text{Effective Cost Price (CP)} = 4,500 + 500 = ₹5,000$.
3. $\text{Selling Price (SP)} = ₹6,000$.
4. Since $\text{SP} > \text{CP}$, there is a profit: $\text{Profit} = 6,000 - 5,000 = ₹1,000$.
5. $\text{Profit }\% = \left(\frac{1,000}{5,000}\right) \times 100 = 20\%$. Correct Option is (A).
2. $\text{Effective Cost Price (CP)} = 4,500 + 500 = ₹5,000$.
3. $\text{Selling Price (SP)} = ₹6,000$.
4. Since $\text{SP} > \text{CP}$, there is a profit: $\text{Profit} = 6,000 - 5,000 = ₹1,000$.
5. $\text{Profit }\% = \left(\frac{1,000}{5,000}\right) \times 100 = 20\%$. Correct Option is (A).
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Question 1 of 10
Exam Standard
If Selling Price (SP) is greater than Cost Price (CP), there is a:
Correct Answer: Option (A)
When SP > CP, the seller receives more than what was spent, generating a profit.
Question 2 of 10
Exam Standard
A boy bought an old bicycle for ₹800 and spent ₹200 on its repair. He then sold it for ₹1,200. Find his profit percentage.
Correct Answer: Option (B)
Total Real CP = Purchase + Repairs = 800 + 200 = ₹1,000. SP = ₹1,200. Profit = ₹200. Profit % = (200 / 1000) × 100 = 20%.
Question 3 of 10
Exam Standard
By selling a watch for ₹720, a shopkeeper loses 10%. What was the cost price of the watch?
Correct Answer: Option (A)
SP = CP × (100 − Loss%)/100 => 720 = CP × 90/100 => CP = (720 × 100) / 90 = ₹800.
Question 4 of 10
Exam Standard
An article was bought for ₹450 and sold for ₹500. Find the profit amount.
Correct Answer: Option (B)
Profit = SP − CP = 500 − 450 = ₹50.
Question 5 of 10
Exam Standard
The cost price of 10 pens is equal to the selling price of 8 pens. Find the profit percentage.
Correct Answer: Option (B)
Let CP of 1 pen = ₹1. CP of 8 pens = ₹8. SP of 8 pens = CP of 10 pens = ₹10. Profit on 8 pens = 10 − 8 = ₹2. Profit % = (2 / 8) × 100 = 25%.
Question 6 of 10
Exam Standard
A merchant sells an item for ₹540, gaining 20%. Find the cost price.
Correct Answer: Option (B)
CP = (SP × 100) / (100 + Gain%) = (540 × 100) / 120 = 4.5 × 100 = ₹450.
Question 7 of 10
Exam Standard
Find the selling price when CP = ₹650 and Loss = 8%.
Correct Answer: Option (A)
Loss = 8% of 650 = 52. SP = 650 − 52 = ₹598.
Question 8 of 10
Exam Standard
If a shopkeeper sells 1 kg sugar at cost price but uses a 900 g weight, what is his gain percentage?
Correct Answer: Option (B)
Gain % = [Error / (True Value − Error)] × 100 = (100 / 900) × 100 = 100 / 9 = 11 1/9%.
Question 9 of 10
Exam Standard
A radio was purchased for ₹800 and sold for ₹760. Find the loss percentage.
Correct Answer: Option (B)
Loss = 800 − 760 = ₹40. Loss % = (40 / 800) × 100 = 5%.
Question 10 of 10
Exam Standard
Which of the following is the correct formula for Profit %?
Correct Answer: Option (B)
Profit % is always calculated strictly on Cost Price: (Profit / CP) × 100.
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Last-Minute Cadet Revision Matrix
Rapid recall checkpoints to review 24 hours before stepping into the examination hall.
| Concept Checkpoint | High-Yield Exam Rule & Memory Anchor |
|---|---|
| Overhead Rule | Overhead expenses must ALWAYS be added to the purchase price to obtain the actual Cost Price. |
| Denominator Rule | Both profit percentage and loss percentage are strictly calculated with CP in the denominator. |
| Twin Sale Law | Selling two articles at same SP with equal profit% and loss% always yields a net loss of (x/10)%. |
| Break-Even | When SP = CP, Profit = 0 and Loss = 0 (No profit, no loss). |
Frequently Asked Questions
How many questions from Profit and Loss appear in the AISSEE Class VI exam?
Typically, 2 to 3 questions directly test Profit and Loss in the 50-question Mathematics paper, contributing 6 to 9 marks towards the 150-mark section total.
Is there any negative marking for incorrect answers in AISSEE Class VI?
No. The National Testing Agency (NTA) does not apply negative marking in the AISSEE Class VI entrance examination. Candidates should attempt every single question.
What is the best way to revise Profit and Loss before the exam?
Review the high-yield formulas, practice the 10 interactive drill MCQs on this page, and memorize the revision checkpoints matrix.