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Agniveer Army CEE Successive Profit & Loss

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This page covers Agniveer Army CEE Successive Profit & Loss with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Successive Profit & Loss— Rules & Concept

Core ConceptRead 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.

Formula BlockMemorise — 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
Exam PatternsWhat 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.

ShortcutsUse 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.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

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

2
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%

3
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%

Exam TrapsCommon mistakes students make — avoid these

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 to Remember

  • 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-Specific Tips

  • 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
Practice MCQs

Successive Profit & Loss — Practice Questions

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A trader buys goods for ₹1000 and sells them at 20% profit. The buyer then sells the same goods at 15% loss. What is the final selling price?

Practice 2easy

A retailer buys a watch for ₹2000 and sells it at 30% profit to a customer. That customer later sells it at 10% loss. At what price did the final customer buy the watch?

Practice 3easy

A shopkeeper buys a shirt for ₹400. He sells it at a profit of 25%. Later, he buys the same shirt back from a customer at 20% loss and sells it again at a profit of 10%. What is his total profit or loss in this transaction?

Practice 4medium

A trader bought an item for ₹500. He sold it at a 30% profit to a customer. The customer then resold it at a 25% loss. What was the customer's selling price?

Practice 5medium

A manufacturer sold an item at a 20% profit to a wholesaler for ₹1200. The wholesaler sold it to a retailer at a 10% profit. What was the manufacturer's cost price?

Practice 6medium

A shopkeeper bought a shirt for ₹400. He sold it at a profit of 25%, and the buyer resold it at a loss of 20%. What was the final selling price?

Practice 7medium

A merchant purchased goods for ₹2000 and sold them at a 15% profit. The buyer then sold these goods at a 10% loss. What was the overall profit or loss percentage for the merchant?

Practice 8hard

A shopkeeper buys a shirt for ₹400. He sells it at a profit of 25%, and the buyer resells it at a loss of 20%. What is the final selling price?

60-Second Revision — Successive Profit & Loss

  • 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
←False Weight / Fraudulent Dealer
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