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Special Market Price Problems

Introduction

Special Market Price Problems involve markups, single or successive discounts, and trade/cash discounts. These problems test your ability to apply percentages step by step in the correct sequence (from Cost Price → Marked Price → Discounts → Selling Price). They are important because they closely reflect real-life market and retail practices.

Pattern: Special Market Price Problems

Pattern

The key is: calculate Marked Price (MP) from Cost Price (CP), then apply each discount in sequence to find Selling Price (SP).

Formulas to remember:
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

A shopkeeper buys an article at ₹800. He marks it 40% above cost and offers two successive discounts of 20% and 10%. On the discounted price, he also gives a 5% trade discount. Find the final Selling Price (SP) and overall profit or loss percentage.

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. Compare single discount vs successive discounts (successive gives less reduction).
  • 2. Apply trade discount first, then cash discount.
  • 3. Reverse problems: given SP, find required markup or MP.
  • 4. Mixed conditions: different markups on different articles.

Trick to Always Use

  • Step 1 → Convert every discount into a multiplier (e.g., 20% → 0.8).
  • Step 2 → Multiply sequentially to get final SP.
  • Step 3 → Compare SP with CP to decide profit or loss.

Summary

Summary

  • Always calculate MP from CP first.
  • Successive discounts are multiplicative, not additive.
  • Apply trade/cash discounts carefully in the given sequence.
  • Compare final SP with CP to determine overall profit or loss.

Example to remember: 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.

Mock Test

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