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Marked Price, Discount & Profit

Introduction

कई real-life और exam questions में Marked Price (MP), दिए गए Discount और अंतिम Profit या Loss शामिल होते हैं।

Marked Price वह price होता है जो किसी item पर लिखा होता है। Shops आमतौर पर MP पर एक discount % देती हैं। Discount लगाने के बाद shopkeeper product को बेचता है और फिर उसे Cost Price (CP) के आधार पर profit या loss होता है।

Pattern: Marked Price, Discount & Profit

Pattern

Discount = MP × (Discount% ÷ 100)

Selling Price (SP) = MP - Discount

Profit or Loss = SP - CP

Profit% = (Profit ÷ CP) × 100

Loss% = (Loss ÷ CP) × 100

Step-by-Step Example

Question

एक article की Marked Price ₹800 है। Shopkeeper 10% का discount देता है और फिर भी 20% का profit कमाता है। Cost Price ज्ञात करें।

Options:

  • A. ₹500
  • B. ₹600
  • C. ₹650
  • D. ₹700

Solution

  1. Step 1: Compute selling price from marked price

    MP = 800, Discount = 10% → Discount amount = 800 का 10% = ₹80. SP = 800 - 80 = ₹720.

  2. Step 2: Reverse profit% to find cost price

    Profit% = 20% का मतलब है SP = CP × 1.2. इसलिए CP = SP ÷ 1.2 = 720 ÷ 1.2 = ₹600.

  3. Final Answer:

    ₹600 → Option B

  4. Quick Check:

    Profit = 720 - 600 = 120 → (120 ÷ 600) × 100 = 20% ✅

Question

एक watch की Marked Price ₹2,000 है। उस पर 15% का discount दिया जाता है। यदि Cost Price ₹1,500 है, तो Profit या Loss % ज्ञात करें।

Options:

  • A. Profit ₹150 (10%)
  • B. Profit ₹200 (13.33%)
  • C. Loss ₹100 (-6.67%)
  • D. Profit ₹250 (16.67%)

Solution

  1. Step 1: Compute selling price from marked price

    MP = 2000, Discount = 15% → Discount amount = 2000 का 15% = ₹300. SP = 2000 - 300 = ₹1,700.

  2. Step 2: Find absolute profit or loss

    Profit = SP - CP = 1,700 - 1,500 = ₹200.

  3. Step 3: Convert to percentage over CP

    Profit% = (200 ÷ 1,500) × 100 = 13.33%.

  4. Final Answer:

    Profit = ₹200 (13.33%) → Option B

  5. Quick Check:

    1,500 का 13.33% लगभग 200 → 1,500 + 200 = 1,700 ✅

Quick Variations

- यदि Profit% और Discount% दिए हों, तो SP = MP × (1 - Discount%).

- और CP = SP ÷ (1 + Profit%).

- यदि Loss% दिया हो, तो CP = SP ÷ (1 - Loss%).

- हमेशा base value का ध्यान रखें: Discount MP पर लगता है, Profit/Loss CP पर।

Trick to Always Use

  • Step 1: SP = MP × (1 - d/100) निकालें।
  • Step 2: SP और CP compare करें → Profit या Loss।
  • Step 3: Reverse calculation के लिए CP = SP ÷ (1 ± p/100) उपयोग करें।

Summary

Summary

  • SP निकालें: SP = MP - (MP × d/100).
  • SP और CP compare करके Profit/Loss ज्ञात करें: Profit/Loss = SP - CP.
  • Percentage हमेशा CP के आधार पर निकाली जाती है: Profit% = (Profit ÷ CP) × 100.
  • Reverse problems में CP = SP ÷ (1 ± p/100) formula उपयोग करें।

याद रखने योग्य उदाहरण:
MP = ₹800, 10% discount → SP = ₹720; 20% profit पर CP = ₹600.

Practice

(1/5)
1. A shirt is marked at ₹1,000. A shopkeeper offers a 10% discount. Find the Selling Price.
easy
A. ₹900
B. ₹950
C. ₹1,100
D. ₹1,050

Solution

  1. Step 1: Calculate discount amount

    Discount = 10% of 1000 = 100.

  2. Step 2: Subtract discount from MP

    SP = 1000 - 100 = ₹900.

  3. Final Answer:

    ₹900 → Option A

  4. Quick Check:

    90% of 1000 = 900 ✅
Hint: SP = MP × (1 - d/100).
Common Mistakes: Subtracting discount% directly from MP instead of value.
2. A bag has a Marked Price of ₹2,000. A 20% discount is given. What is the Selling Price?
easy
A. ₹1,500
B. ₹1,600
C. ₹1,700
D. ₹1,800

Solution

  1. Step 1: Calculate discount amount

    Discount = 20% of 2000 = 400.

  2. Step 2: Compute selling price

    SP = 2000 - 400 = ₹1,600.

  3. Final Answer:

    ₹1,600 → Option B

  4. Quick Check:

    80% of 2000 = 1600 ✅
Hint: Directly multiply MP × (100 - d)% ÷ 100.
Common Mistakes: Calculating 20% as 200 instead of 400.
3. A watch has MP ₹1,500. Discount 15%. Cost Price = ₹1,200. Find Profit or Loss.
easy
A. ₹30 Loss
B. ₹30 Profit
C. ₹75 Profit
D. ₹75 Loss

Solution

  1. Step 1: Find selling price after discount

    SP = 1500 - (15% of 1500) = 1500 - 225 = 1275.

  2. Step 2: Compare SP and CP

    Profit = SP - CP = 1275 - 1200 = ₹75.

  3. Final Answer:

    ₹75 → Option C

  4. Quick Check:

    Profit% = 75 ÷ 1200 × 100 = 6.25% ✅
Hint: Profit = SP - CP after discount.
Common Mistakes: Subtracting discount from CP instead of MP.
4. A cycle is marked at ₹2,400 with a 25% discount. If CP = ₹1,600, find Profit%.
medium
A. 12.5%
B. 15%
C. 20%
D. 25%

Solution

  1. Step 1: Compute selling price

    SP = 2400 - (25% of 2400) = 2400 - 600 = 1800.

  2. Step 2: Compute absolute profit

    Profit = 1800 - 1600 = 200.

  3. Step 3: Convert to percentage

    Profit% = (200 ÷ 1600) × 100 = 12.5%.

  4. Final Answer:

    12.5% → Option A

  5. Quick Check:

    12.5% of 1600 = 200 → CP + 200 = 1800 ✅
Hint: Always use formula Profit% = (Profit ÷ CP) × 100.
Common Mistakes: Taking profit% on MP instead of CP.
5. A laptop MP ₹40,000, discount 10%. If CP = ₹34,000, find Profit%.
medium
A. 5%
B. 6%
C. 7%
D. 8%

Solution

  1. Step 1: Compute SP after discount

    SP = 40000 - (10% of 40000) = 40000 - 4000 = 36000.

  2. Step 2: Compute profit

    Profit = 36000 - 34000 = 2000.

  3. Step 3: Convert to percentage

    Profit% = (2000 ÷ 34000) × 100 ≈ 5.88%.

  4. Final Answer:

    6% → Option B

  5. Quick Check:

    6% of 34000 = 2040 ≈ Profit 2000 ✅
Hint: Round to nearest percent when decimal arises.
Common Mistakes: Writing decimal value without checking nearest option.

Mock Test

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