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Special Market Price Problems

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Introduction

Special Market Price Problems में markups, single या successive discounts, और trade/cash discounts आते हैं। ये problems यह परखती हैं कि आप percentages को सही क्रम में (Cost Price → Marked Price → Discounts → Selling Price) चरण दर चरण apply कर पाते हैं या नहीं। ये महत्वपूर्ण हैं क्योंकि ये असली market और retail प्रैक्टिस को अच्छी तरह दर्शाते हैं।

Pattern: Special Market Price Problems

Pattern: Special Market Price Problems

मुख्य बात: Marked Price (MP) को Cost Price (CP) से निकालें, फिर क्रमवार प्रत्येक discount apply करके Selling Price (SP) खोजें।

याद रखने वाली formulas:
MP = CP × (1 + Markup%)
SP (single discount) = MP × (1 - d%)
SP (successive discounts d1 and d2) = MP × (1 - d1) × (1 - d2)

Step-by-Step Example

Question

एक shopkeeper किसी article को ₹800 में खरीदता है। वह उसे cost से 40% ऊपर mark करता है और दो successive discounts 20% और 10% देता है। डिस्काउंट के बाद वह discounted price पर 5% trade discount भी देता है। अंतिम Selling Price (SP) और कुल profit या loss percentage क्या होगा?

Options:

  • A. SP ≈ ₹765.08; Loss ≈ 4.37%
  • B. SP ≈ ₹806; Loss ≈ 1%
  • C. SP ≈ ₹900; Profit ≈ 12.5%
  • D. SP ≈ ₹840; No profit, no loss

Solution

  1. Step 1: Calculate Marked Price (MP)

    MP = 800 × 1.4 = ₹1,120.

  2. Step 2: Apply first discount (20%)

    SP₁ = 1,120 × 0.80 = ₹896.

  3. Step 3: Apply second discount (10%)

    SP₂ = 896 × 0.90 = ₹806.40.

  4. Step 4: Apply trade discount (5%)

    Final SP = 806.40 × 0.95 = ₹765.08.

  5. Step 5: Compare with CP

    CP = ₹800 → Loss = 800 - 765.08 = ₹34.92.

  6. Step 6: Compute overall loss %

    Loss % = (34.92 ÷ 800) × 100 = 4.37% loss.

  7. Final Answer:

    Final SP ≈ ₹765.08; Overall ≈ 4.37% loss → Option A

  8. Quick Check:

    800 × (1.4 × 0.8 × 0.9 × 0.95) ≈ 765 ✔️

Quick Variations

  • 1. Single discount और successive discounts की तुलना करें (successive ज्यादातर कम reduction देता है)।
  • 2. Trade discount पहले लगाकर cash discount बाद में लगाना भी दिया जा सकता है-sequence का ध्यान रखें।
  • 3. Reverse problems: यदि अंतिम SP दिया हो तो आवश्यक markup या MP क्या होगी, यह निकालें।
  • 4. Mixed conditions: अलग-अलग articles पर अलग markups लग सकते हैं।

Trick to Always Use

  • Step 1 → हर discount को multiplier में बदलें (जैसे 20% → 0.8)।
  • Step 2 → क्रमवार multiply करके अंतिम SP पाएं।
  • Step 3 → अंतिम SP को CP से compare करें और profit/loss तय करें।

Summary

  • हमेशा पहले MP को CP से calculate करें।
  • Successive discounts additive नहीं होते-वे multiplicative होते हैं।
  • Trade/cash discounts को दिए गए अनुक्रम में सावधानी से लागू करें।
  • अंत में अंतिम SP को CP से compare करके कुल profit या loss पता करें।

याद रखने के लिए उदाहरण: CP 800 → MP 1120 → 20% → 10% → 5% → Final SP ≈ 765

Practice

(1/5)
1. A trader buys an article for ₹500. He marks it 20% above cost and gives a 10% discount. Find the Selling Price.
easy
A. ₹540
B. ₹550
C. ₹560
D. ₹600

Solution

  1. Step 1: Compute Marked Price (MP)

    MP = 500 × 1.20 = ₹600.

  2. Step 2: Apply discount

    SP = 600 × 0.90 = ₹540.

  3. Final Answer:

    ₹540 → Option A

  4. Quick Check:

    540 - 500 = ₹40 profit (8% of CP) ✅
Hint: Compute MP first, then apply discount multiplier.
Common Mistakes: Applying discount on CP instead of MP.
2. A shopkeeper buys goods worth ₹800. He marks them 25% above cost and allows 20% discount. Find the Selling Price.
easy
A. ₹760
B. ₹800
C. ₹820
D. ₹840

Solution

  1. Step 1: Compute Marked Price (MP)

    MP = 800 × 1.25 = ₹1,000.

  2. Step 2: Apply discount

    SP = 1,000 × 0.80 = ₹800.

  3. Final Answer:

    ₹800 → Option B

  4. Quick Check:

    SP = CP → No profit, no loss ✅
Hint: Apply discount on MP (not on CP).
Common Mistakes: Comparing markup% and discount% directly instead of calculating SP.
3. A trader marks an article at ₹1,200 and allows successive discounts of 10% and 20%. Find the Selling Price.
easy
A. ₹840
B. ₹850
C. ₹864
D. ₹900

Solution

  1. Step 1: Apply first discount

    After 10% discount → 1,200 × 0.90 = 1,080.

  2. Step 2: Apply second discount

    After 20% discount → 1,080 × 0.80 = ₹864.

  3. Final Answer:

    ₹864 → Option C

  4. Quick Check:

    Effective multiplier = 0.9 × 0.8 = 0.72 → 1,200 × 0.72 = 864 ✅
Hint: Multiply successive discount factors (e.g., 0.9 × 0.8).
Common Mistakes: Adding discounts (10% + 20% = 30%) instead of compounding.
4. A shopkeeper buys an item for ₹1,000, marks it up by 50%, and offers two successive discounts of 20% and 10%. Find the Selling Price.
medium
A. ₹960
B. ₹972
C. ₹990
D. ₹1,080

Solution

  1. Step 1: Compute MP after markup

    MP = 1,000 × 1.50 = ₹1,500.

  2. Step 2: Apply first discount (20%)

    1,500 × 0.80 = 1,200.

  3. Step 3: Apply second discount (10%)

    1,200 × 0.90 = ₹1,080.

  4. Final Answer:

    ₹1,080 → Option D

  5. Quick Check:

    Multiplier = 1.5 × 0.8 × 0.9 = 1.08 → 1,000 × 1.08 = 1,080 ✅
Hint: Apply markup first, then multiply successive discount factors.
Common Mistakes: Adding discounts or applying them in wrong order.
5. A trader buys an article at ₹2,000, marks it at 40% above cost, and allows a 25% discount. Find his profit or loss percent.
medium
A. 5% profit
B. 10% profit
C. 5% loss
D. 10% loss

Solution

  1. Step 1: Compute Marked Price (MP)

    MP = 2,000 × 1.40 = ₹2,800.

  2. Step 2: Apply discount

    SP = 2,800 × 0.75 = ₹2,100.

  3. Step 3: Compute profit

    Profit = 2,100 - 2,000 = ₹100.

  4. Step 4: Compute profit %

    Profit % = (100 ÷ 2,000) × 100 = 5% profit.

  5. Final Answer:

    5% profit → Option A

  6. Quick Check:

    SP > CP → Profit confirmed (100/2000 = 5%) ✅
Hint: Compute MP then apply discount; compare SP with CP for profit% calculation.
Common Mistakes: Subtracting discount% from markup% instead of calculating SP.