Successive Discounts

🎯 Learning Objective

Convert two or more successive discounts into a single discount and compare offers.

💡 Concept

• Successive discounts a% and b% → single discount = a + b − ab/100
• Both are decreases, so the combined effect is always LESS than a + b
• Three discounts → apply the formula twice, or multiply MFs: (1−a/100)(1−b/100)(1−c/100)
• A flat (a + b)% discount is always BETTER for the customer than successive a% and b%

🧮 Key Formulas

Single discount = a + b − ab/100

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SP = MP × (1 − a/100) × (1 − b/100)

✏️ Easy Example

Q. Find the single discount equivalent to successive discounts of 20% and 10%.

1. Single = 20 + 10 − (20 × 10)/100
2. = 30 − 2

Answer: 28%

🇮🇳 Real-Life Example

A '50% + 20% OFF' sale banner is NOT 70% off — the formula gives 50 + 20 − 10 = 60% off. Check every mega-sale banner yourself now.

📝 Exam-Level Example

Q. An item marked at ₹2,000 is sold after successive discounts of 20% and 15%. Find the selling price.

1. After 20%: 2000 × 0.80 = 1600
2. After 15%: 1600 × 0.85 = 1360

Answer: ₹1,360

📝 Exam-Level Example

Q. Which is better for a customer — a single discount of 40%, or successive discounts of 25% and 15%?

1. Successive = 25 + 15 − (25 × 15)/100
2. = 40 − 3.75 = 36.25%
3. 40% > 36.25%

Answer: Single 40% discount is better

🪄 Memory Trick

Successive discounts NEVER simply add — the answer is always a + b − ab/100. In compare questions, the flat sum wins for the buyer every time.

⚠️ Common Mistakes

• ❌ Adding successive discounts directly (20 + 10 = 30 ✗, correct is 28)
• ❌ Applying the second discount on the original MP instead of the reduced price
• ❌ Forgetting that the formula needs minus signs for a discount-plus-markup mix

🏆 Exam Tips

• ✅ For odd numbers of discounts, chain the MFs — fewer sign errors than the formula
• ✅ Memorise favourites: 10+10→19%, 20+10→28%, 20+20→36%, 50+20→60%

📌 Summary

• Two discounts → a + b − ab/100, always less than a + b
• Three or more → multiply the MFs
• Flat (a+b)% beats successive a%, b% for the customer
• Second discount applies on the already-reduced price