Percentage Increase & Decrease

🎯 Learning Objective

Compute % change and apply multiplying factors for quick increase/decrease calculations.

💡 Concept

• % change = (Change / Original) × 100 — original is ALWAYS the base
• Increase by 20% → multiply by 1.20; decrease by 20% → multiply by 0.80
• Multiplying factor (MF) method turns word problems into one multiplication
• If price ↑ x%, consumption must ↓ [x/(100+x)]×100 % to keep expenditure same

🧮 Key Formulas

% change = (change/original) × 100

>

↑x% → ×(1 + x/100)

>

↓x% → ×(1 − x/100)

✏️ Easy Example

Q. A ₹500 shirt's price increases by 15%. Find the new price.

1. MF = 1.15
2. 500 × 1.15 = 575

Answer: ₹575

🇮🇳 Real-Life Example

Petrol goes from ₹90 to ₹99 → change 9 on base 90 = 10% hike. News channels calculate exactly this.

📝 Exam-Level Example

Q. The price of sugar rises by 25%. By what % should a family cut consumption to keep expenditure unchanged?

1. Cut % = [25/(100+25)] × 100
2. = (25/125) × 100 = 20

Answer: 20%

📝 Exam-Level Example

Q. A number decreased by 30% gives 84. Find the number.

1. N × 0.70 = 84
2. N = 84 ÷ 0.7

Answer: 120

🪄 Memory Trick

25% ↑ = 1/4 ↑ → cut = 1/5 = 20%. Fraction pairs: 1/4↔1/5, 1/3↔1/4, 1/2↔1/3. Numerator same, denominator +1.

⚠️ Common Mistakes

• ❌ Taking new value as base for % change
• ❌ Adding percentages of different bases directly

🏆 Exam Tips

• ✅ MF method: chain multiple changes as factor products
• ✅ x% increase then x% decrease NEVER cancels out — net is always a decrease

📌 Summary

• Base = original, always
• ↑x% → ×(1+x/100); ↓x% → ×(1−x/100)
• Expenditure-constant cut = x/(100+x) × 100
• Fraction pairs make it 5-second work