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Successive Profit & Loss

CRPF Constable · Quantitative Aptitude

Also prepare for:BSF Const CISF Const ITBP Const UP Const

← False Weight / Fraudulent Dealer

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Core Concept

Read this first — the foundation of the topic

→Core Concept

When profits and losses are applied one after another, we cannot simply add or subtract the percentages. Each percentage change acts on the new value, not the original price

💡Key Rules

If successive changes of a% and b% occur, the net effect formula is: Net% = a + b + (ab)/100. Use positive values for profit and negative values for loss. For three successive changes a%, b%, c%, first find net effect of any two, then apply the third change.

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Formula Block

Memorise — at least one formula appears in every paper

• Two successive changes: Net% = a + b + (ab)/100

• Selling price after successive changes: SP = CP × (100+a)/100 × (100+b)/100

• Overall profit/loss = Net% of original cost price

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Exam Patterns

What examiners ask — read before attempting PYQs

Questions typically involve 2-3 successive transactions. Common scenarios include buying-selling chains, discount followed by profit, or multiple markups. SSC often asks for overall profit/loss percentage or final selling price.

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Shortcuts

Use these to save 30–60 seconds per question

For quick calculation, convert percentages to multipliers. 20% profit = 1.2, 10% loss = 0.9. Multiply all factors: 1.2 × 0.9 = 1.08 = 8% overall profit.

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Worked Example

Solve this step-by-step before moving on

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Step 1

Identify the changes First transaction: +20% (profit) Second transaction: -10% (loss)

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Step 2

Apply the formula Net% = a + b + (ab)/100 Net% = 20 + (-10) + (20 × (-10))/100 Net% = 20 - 10 - 200/100 Net% = 10 - 2 = 8%

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Step 3

Verify using multiplier method Final value = 1000 × 1.20 × 0.90 = 1000 × 1.08 = 1080 Profit = 1080 - 1000 = 80 Profit% = 80/1000 × 100 = 8% Answer: 8% overall profit Alternate Method using SP calculation: After first sale: 1000 × 120/100 = 1200 After second sale: 1200 × 90/100 = 1080 Net profit = 1080 - 1000 = 80 Profit% = 8% Common Mistake: Students often add percentages directly (20% - 10% = 10%) ignoring the compounding effect. Always remember that each subsequent percentage works on the changed value, not the original price. The interaction term (ab)/100 is crucial and frequently overlooked.

🔑 Key Points

Successive changes cannot be added directly due to compounding effect
Formula for two changes: Net% = a + b + (ab)/100
Use positive values for profit, negative for loss in the formula
Multiplier method: Convert percentages to decimals and multiply
Each subsequent change acts on the new value, not original price
Interaction term (ab)/100 is often the key to correct answers
Three changes: Find net of first two, then apply third change
Final amount = Original × (100+a)/100 × (100+b)/100

📌 Exam Facts

Net percentage formula for successive changes: a + b + (ab)/100
20% profit converts to multiplier 1.2, 25% loss converts to 0.75
For equal successive profits of x%, net effect is x + x + x²/100
Two successive discounts of 10% each give net discount of 19%
Successive changes of +50% and -20% result in +20% net change
Three successive profits of 10% each give net profit of 33.1%
Formula remains same whether dealing with CP, SP, or marked price

🚀 60-Second Revision

Remember: Net% = a + b + (ab)/100 for two successive changes
Trick: Use multipliers for faster calculation - multiply all factors
Formula: SP = CP × (100+a)/100 × (100+b)/100
Trap: Never add successive percentages directly
Method: For three changes, find net of any two first, then apply third
Quick check: Positive result means profit, negative means loss

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