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Discount on Marked Price (Single Discount)

Introduction

In many shopping or business scenarios, an item is sold at a discount on its marked price (MP). This type of problem is very common in aptitude tests.

The key idea is that the discount is always calculated on the marked price. The final selling price (SP) is the marked price minus the discount amount.

Pattern: Discount on Marked Price (Single Discount)

Pattern

The shopkeeper reduces the marked price by a certain percentage to arrive at the selling price.

Formula: Selling Price = Marked Price × (1 - Discount%/100)
Discount Amount: = Marked Price × (Discount% ÷ 100)

Step-by-Step Example

Question

A shirt has a marked price of ₹1,200. The shopkeeper offers a discount of 15%. Find the selling price.

Options:

  • A. ₹1,000
  • B. ₹1,010
  • C. ₹1,020
  • D. ₹1,030

Solution

  1. Step 1: Identify marked price and discount.

    Marked Price (MP) = ₹1,200, Discount = 15%.

  2. Step 2: Compute the discount amount.

    Discount amount = (15 ÷ 100) × 1200 = ₹180.

  3. Step 3: Subtract discount from MP to get SP.

    Selling Price = MP - Discount = 1200 - 180 = ₹1,020.

  4. Final Answer:

    ₹1,020 → Option C

  5. Quick Check:

    85% of 1200 = 0.85 × 1200 = 1020 ✅

Quick Variations

- If discount is 25% on ₹800 → SP = 75% of 800 = ₹600.

- If discount is 10% on ₹1,500 → SP = 90% of 1500 = ₹1,350.

- If discount is 12.5% on ₹2,000 → SP = 87.5% of 2000 = ₹1,750.

Trick to Always Use

  • Shortcut: Selling Price = (100 - d)% of Marked Price.
  • Tip: Use complement % to avoid subtraction mistakes (e.g., for 20% discount, SP = 80% of MP).
  • Memory Aid: Always apply discount on MP, not on cost price or profit price.

Summary

Summary

  • Compute discount amount: Discount = MP × (d ÷ 100).
  • Find selling price: SP = MP - Discount or SP = MP × (1 - d/100).
  • Use complement percent (100 - d)% to calculate SP quickly.
  • Always apply the discount on the Marked Price (MP), not on CP or SP).

Example to remember:
MP = ₹1,200, d = 15% → SP = ₹1,200 × 0.85 = ₹1,020.

Practice

(1/5)
1. A toy is marked at ₹500. A discount of 10% is given. Find the selling price.
easy
A. ₹450
B. ₹400
C. ₹475
D. ₹420

Solution

  1. Step 1: Identify MP and discount %.

    Marked Price = ₹500, Discount = 10%.

  2. Step 2: Calculate the discount amount.

    Discount amount = (10 ÷ 100) × 500 = ₹50.

  3. Step 3: Subtract discount from MP to get SP.

    Selling Price = 500 - 50 = ₹450.

  4. Final Answer:

    Selling Price = ₹450 → Option A

  5. Quick Check:

    90% of 500 = 450 ✅
Hint: Selling Price = (100 - discount%) × MP ÷ 100.
Common Mistakes: Forgetting to subtract discount from MP or applying discount on wrong base.
2. A bag is marked at ₹800. It is sold at a discount of 20%. Find the selling price.
easy
A. ₹600
B. ₹640
C. ₹700
D. ₹720

Solution

  1. Step 1: Note MP and discount rate.

    Marked Price = ₹800, Discount = 20%.

  2. Step 2: Compute the discount amount.

    Discount amount = (20 ÷ 100) × 800 = ₹160.

  3. Step 3: Subtract discount from MP.

    Selling Price = 800 - 160 = ₹640.

  4. Final Answer:

    Selling Price = ₹640 → Option B

  5. Quick Check:

    80% of 800 = 640 ✅
Hint: Shortcut: SP = (100 - d)% of MP.
Common Mistakes: Mistaking 20% of 800 as 200 instead of 160.
3. A shirt has a marked price of ₹1,200. If a discount of 15% is given, what is the selling price?
easy
A. ₹1,000
B. ₹1,050
C. ₹1,020
D. ₹1,080

Solution

  1. Step 1: Identify MP and discount.

    Marked Price = ₹1200, Discount = 15%.

  2. Step 2: Calculate discount amount.

    Discount amount = (15 ÷ 100) × 1200 = ₹180.

  3. Step 3: Subtract to find SP.

    Selling Price = 1200 - 180 = ₹1020.

  4. Final Answer:

    Selling Price = ₹1020 → Option C

  5. Quick Check:

    85% of 1200 = 1020 ✅
Hint: When % is easy (like 15%), split into 10% + 5% of MP.
Common Mistakes: Subtracting percentage directly (1200 - 15) instead of calculating 15%.
4. A watch is marked at ₹2,000. The shopkeeper offers a 12.5% discount. Find the selling price.
medium
A. ₹1,750
B. ₹1,800
C. ₹1,700
D. ₹1,850

Solution

  1. Step 1: Record MP and discount rate.

    Marked Price = ₹2000, Discount = 12.5%.

  2. Step 2: Find discount amount.

    Discount amount = (12.5 ÷ 100) × 2000 = ₹250.

  3. Step 3: Compute selling price.

    Selling Price = 2000 - 250 = ₹1750.

  4. Final Answer:

    Selling Price = ₹1750 → Option A

  5. Quick Check:

    87.5% of 2000 = 1750 ✅
Hint: 12.5% = 1/8, so subtract 1/8 of MP quickly.
Common Mistakes: Treating 12.5% as 12 or 13 instead of fraction 1/8.
5. A pair of shoes is marked at ₹1,500. A discount of 20% is given. What is the selling price?
medium
A. ₹1,100
B. ₹1,150
C. ₹1,200
D. ₹1,250

Solution

  1. Step 1: Identify MP and discount %.

    Marked Price = ₹1500, Discount = 20%.

  2. Step 2: Compute discount amount.

    Discount amount = (20 ÷ 100) × 1500 = ₹300.

  3. Step 3: Find SP after discount.

    Selling Price = 1500 - 300 = ₹1200.

  4. Final Answer:

    Selling Price = ₹1200 → Option C

  5. Quick Check:

    80% of 1500 = 1200 ✅
Hint: For 20% discount, SP = 4/5 of MP.
Common Mistakes: Subtracting 20 instead of 20% of MP.

Mock Test

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