Successive Percentage Change
Successive percentage change
Learning Objective
Apply the a + b + ab/100 formula for two successive changes.
🎯 Learning Objective
Apply the a + b + ab/100 formula for two successive changes.
💡 Concept
- Two successive changes a% and b% → net = a + b + ab/100 (use signs!)
- Increase 20% then decrease 20%: 20 − 20 − 400/100 = −4% (net decrease)
- Population/price applying same rate twice = compound growth
- Area of rectangle when sides change: same formula with the two side-changes
🧮 Key Formulas
Net % = a + b + (ab)/100
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Equal ↑ then ↓ by x% → net ↓ x²/100 %
✏️ Easy Example
Q. A price increases 10% and then 20%. Find the net increase.
- Net = 10 + 20 + (10×20)/100
- = 30 + 2
Answer: 32%
🇮🇳 Real-Life Example
Flipkart 'extra 20% off on 30% off' is NOT 50% off — it's 30+(−20)+... = 44% off. Now you can check every sale banner.
📝 Exam-Level Example
Q. The length of a rectangle increases 20% and breadth decreases 10%. What happens to the area?
- Net = 20 + (−10) + (20×−10)/100
- = 10 − 2 = 8
Answer: Increases by 8%
📝 Exam-Level Example
Q. A number is increased by 25% and then decreased by 25%. Net change?
- Net = −(25²)/100 = −625/100
Answer: 6.25% decrease
🪄 Memory Trick
Same % up then down by x → always down by x²/100. 10→1%, 20→4%, 25→6.25%, 30→9%.
⚠️ Common Mistakes
- ❌ Adding successive percentages directly (20+20=40 ✗)
- ❌ Dropping the minus sign for decreases
🏆 Exam Tips
- ✅ Works for any two changes: price, population, area
- ✅ Three changes → apply the formula twice
📌 Summary
- Net = a + b + ab/100 with signs
- Equal up-down by x → loss of x²/100
- Discount-on-discount uses the same formula