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Successive Discounts

Introduction

कई shopping problems में, किसी product को पहले एक discount पर बेचा जाता है, और फिर कम हुई price पर एक और discount लगाया जाता है। इन्हें successive discounts कहा जाता है।

Students अक्सर सीधे discounts को जोड़ देते हैं, लेकिन सही तरीका है कि उन्हें एक-एक करके apply किया जाए या net discount formula का उपयोग किया जाए।

Pattern: Successive Discounts

Pattern

जब दो discounts x% और y% को successively apply किया जाता है, तो net discount होता है:

Net Discount = x + y - (x·y / 100)

दूसरा तरीका यह है कि पहले पहले discount से price reduce करें, फिर reduced price पर दूसरा discount लगाएँ।

Step-by-Step Example

Question

एक shirt की marked price ₹500 है। उस पर 20% और 10% के successive discounts दिए जाते हैं। Selling price ज्ञात करें।

Options:

  • A. ₹350
  • B. ₹360
  • C. ₹380
  • D. ₹400

Solution

  1. Step 1: Apply the first discount

    पहला discount 20% है → 1st discount के बाद price = 500 × (80/100) = ₹400.

  2. Step 2: Apply the second discount

    दूसरा discount 10% है → 2nd discount के बाद price = 400 × (90/100) = ₹360.

  3. Step 3: Use the formula method

    Net discount = 20 + 10 - (20×10)/100 = 28%. Final price = 500 × (72/100) = ₹360 (same result).

  4. Final Answer:

    ₹360 → Option B

  5. Quick Check:

    Net discount 28% → 500 का 28% = 140 → 500 - 140 = 360 ✅

Quick Variations

  • 1. 3 successive discounts x%, y%, z% → Net = x + y + z - (xy + yz + zx)/100 + (xyz)/10000
  • 2. Successive discounts ठीक वैसे ही काम करते हैं जैसे successive percentage decrease problems।

Trick to Always Use

  • Exam में समय बचाने के लिए formula x + y - (x·y / 100) का उपयोग करें।
  • 3 या उससे अधिक discounts के लिए formula को ध्यान से extend करें।
  • हमेशा net discount percentage से quick check कर लें।

Summary

Summary

  • Successive discounts को सीधे जोड़ना सही नहीं है; इन्हें क्रम से apply किया जाता है।
  • दूसरा discount हमेशा reduced price पर लगता है।
  • Calculations को आसान बनाने के लिए Net Discount = x + y - (x·y/100) formula उपयोग करें।
  • Mistakes से बचने के लिए net percentage का cross-check करें।

याद रखने योग्य उदाहरण:
₹500 पर 20% और 10% के discounts → Final Price = ₹360.

Practice

(1/5)
1. A shirt is marked at ₹600. Successive discounts of 10% and 20% are given. Find the selling price.
easy
A. ₹420
B. ₹432
C. ₹450
D. ₹480

Solution

  1. Step 1: Apply first discount

    Apply first discount 10% → Price = 600 × (90/100) = ₹540.

  2. Step 2: Apply second discount

    Apply second discount 20% on reduced price → Price = 540 × (80/100) = ₹432.

  3. Step 3: Verify with formula

    Net discount = 10 + 20 - (10×20)/100 = 28%. Selling price = 600 × (72/100) = ₹432.

  4. Final Answer:

    ₹432 → Option B

  5. Quick Check:

    28% of 600 = 168 → 600 - 168 = 432 ✅
Hint: Use net discount formula or multiply complements: 0.9 × 0.8 = 0.72.
Common Mistakes: Adding discounts directly (10% + 20% = 30%) instead of using successive method.
2. A laptop is marked at ₹50,000. It is sold with successive discounts of 15% and 5%. Find the selling price.
easy
A. ₹39,750
B. ₹40,375
C. ₹40,500
D. ₹42,000

Solution

  1. Step 1: Apply first discount

    First discount 15% → Price = 50,000 × (85/100) = ₹42,500.

  2. Step 2: Apply second discount

    Second discount 5% → Price = 42,500 × (95/100) = ₹40,375.

  3. Step 3: Verify with formula

    Net discount = 15 + 5 - (15×5)/100 = 19.25%. Selling price = 50,000 × (80.75/100) = ₹40,375.

  4. Final Answer:

    ₹40,375 → Option B

  5. Quick Check:

    19.25% of 50,000 = 9,625 → 50,000 - 9,625 = 40,375 ✅
Hint: Apply second discount on the reduced price (not on original).
Common Mistakes: Applying both discounts on original price.
3. A watch is marked at ₹2,000. It is sold with successive discounts of 25% and 10%. Find the selling price.
medium
A. ₹1,200
B. ₹1,300
C. ₹1,350
D. ₹1,400

Solution

  1. Step 1: Apply first discount

    First discount 25% → Price = 2,000 × (75/100) = ₹1,500.

  2. Step 2: Apply second discount

    Second discount 10% → Price = 1,500 × (90/100) = ₹1,350.

  3. Step 3: Verify with formula

    Net discount = 25 + 10 - (25×10)/100 = 32.5%. Selling price = 2,000 × (67.5/100) = ₹1,350.

  4. Final Answer:

    ₹1,350 → Option C

  5. Quick Check:

    32.5% of 2,000 = 650 → 2,000 - 650 = 1,350 ✅
Hint: Multiply complements: 0.75 × 0.90 = 0.675.
Common Mistakes: Adding percentages directly instead of successive calculation.
4. A shopkeeper gives successive discounts of 20% and 15% on a marked price of ₹800. Find the selling price.
medium
A. ₹540
B. ₹560
C. ₹544
D. ₹552

Solution

  1. Step 1: Apply first discount

    First discount 20% → Price = 800 × (80/100) = ₹640.

  2. Step 2: Apply second discount

    Second discount 15% → Price = 640 × (85/100) = ₹544.

  3. Step 3: Verify with formula

    Net discount = 20 + 15 - (20×15)/100 = 32%. Selling price = 800 × (68/100) = ₹544.

  4. Final Answer:

    ₹544 → Option C

  5. Quick Check:

    32% of 800 = 256 → 800 - 256 = 544 ✅
Hint: Use net discount formula for quick verification.
Common Mistakes: Forgetting second discount applies to reduced price.
5. A camera is sold with successive discounts of 30% and 20% on a marked price of ₹10,000. Find the selling price.
medium
A. ₹5,400
B. ₹5,600
C. ₹5,800
D. ₹6,000

Solution

  1. Step 1: Apply first discount

    First discount 30% → Price = 10,000 × (70/100) = ₹7,000.

  2. Step 2: Apply second discount

    Second discount 20% → Price = 7,000 × (80/100) = ₹5,600.

  3. Step 3: Verify with formula

    Net discount = 30 + 20 - (30×20)/100 = 44%. Selling price = 10,000 × (56/100) = ₹5,600.

  4. Final Answer:

    ₹5,600 → Option B

  5. Quick Check:

    44% of 10,000 = 4,400 → 10,000 - 4,400 = 5,600 ✅
Hint: Compute complements product: 0.70 × 0.80 = 0.56.
Common Mistakes: Treating discounts as additive without correction term.

Mock Test

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