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Marked Price, Discount & Profit

Introduction

Many real-life and exam questions involve a Marked Price (MP), a Discount offered, and the resulting Profit or Loss.

The Marked Price is the price printed on the item. Shops usually give a discount % on MP. After applying the discount, the shopkeeper sells the product and makes either a profit or loss depending on the Cost Price (CP).

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

An article has a Marked Price of ₹800. A shopkeeper offers a discount of 10% and still makes a profit of 20%. Find the Cost Price.

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 = 10% of 800 = ₹80. SP = 800 - 80 = ₹720.

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

    Profit% = 20% means SP = CP × (1 + 20/100) = CP × 1.2. So 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

A watch is marked at ₹2,000. It is sold at a discount of 15%. If the Cost Price is ₹1,500, find the Profit or Loss %.

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 = 15% of 2000 = ₹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:

    13.33% of 1,500 ≈ 200 → 1,500 + 200 = 1,700 ✅

Quick Variations

- If Profit% and Discount% are given, SP = MP × (1 - Discount%) and CP = SP ÷ (1 + Profit%).

- If Loss% is given instead, replace with CP = SP ÷ (1 - Loss%).

- Always carefully note the base value: Discount works on MP, Profit/Loss works on CP.

Trick to Always Use

  • Step 1: Calculate SP = MP × (1 - d/100).
  • Step 2: Compare SP with CP → Profit or Loss.
  • Step 3: For reverse calculation, CP = SP ÷ (1 ± p/100).

Summary

Summary

  • Calculate SP from MP first: SP = MP - (MP × d/100).
  • Compare SP with CP to determine absolute Profit/Loss: Profit/Loss = SP - CP.
  • Compute percentage using CP as base: Profit% = (Profit ÷ CP) × 100.
  • For reverse problems, use CP = SP ÷ (1 ± p/100) to recover cost price.

Example to remember:
MP = ₹800, 10% discount → SP = ₹720; 20% profit on CP gives 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.

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