Marked Price and Discount: Formulas, Rules and Questions

Marked Price and Discount deals with the price displayed on an article, the reduction offered on that price, and the final selling price. This page covers the marked price formula, discount percentage, reverse calculations, successive discounts, and questions involving cost price, selling price and profit or loss.

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What Are Marked Price and Discount?

Marked price (MP) is the price written or displayed on an article before any reduction. Discount is the reduction given on the marked price, while the selling price is the amount paid after subtracting the discount.

If the discount is d%, then the selling price is (100 − d)% of the marked price. Thus, SP = MP × (100 − d)/100. For example, a 20% discount on an MP of ₹800 gives a discount of ₹160 and an SP of ₹640.

Marked Price and Discount Formula & Tricks

Important Formulas

Discount amount
Discount = MP − SP

Subtract the selling price from the marked price to obtain the discount in currency units.

Discount percentage
Discount% = (Discount/MP) × 100

The discount percentage is calculated on the marked price, not on the selling price.

Selling price after discount
SP = MP × (100 − d)/100

Here, d is the discount percentage. The customer pays (100 − d)% of the marked price.

Marked price from selling price
MP = SP × 100/(100 − d)

Use this formula when the selling price and discount percentage are given.

Successive discounts
Net discount% = a + b − ab/100

For successive discounts of a% and b%, the equivalent single discount is a + b − ab/100.

Marked price using cost price and profit
MP = CP × (100 + p)/(100 − d)

If the seller earns p% profit after giving d% discount, use CP as the cost price.

Quick Tricks

Use the percentage left after discount

After a discount of d%, the selling price is (100 − d)% of the marked price. This avoids calculating the discount separately when only SP is required.

Example: For MP ₹1,500 and discount 12%, SP = 1,500 × 88/100 = ₹1,320.
Combine successive discounts directly

Two discounts are not added directly because the second discount applies to the reduced price. Use a + b − ab/100.

Example: Successive discounts of 20% and 10% give 20 + 10 − (20 × 10)/100 = 28%, not 30%.
Convert a required profit into marked price

If discount and desired profit are given, equate the selling price expressions: SP = MP(100 − d)/100 and SP = CP(100 + p)/100.

Example: For CP ₹500, 20% profit and 10% discount, MP = 500 × 120/90 = ₹666.67.

Marked Price and Discount Concepts

Marked Price, Discount and Selling Price

The marked price is the listed price, the discount is the reduction from it, and the selling price is the amount remaining after the reduction.

The basic relationship is MP = Discount + SP. If a discount of d% is offered, Discount = d% of MP and SP = (100 − d)% of MP. For MP ₹2,000 and a 15% discount, discount = ₹300 and SP = ₹1,700.

Example: A shirt marked at ₹2,400 is sold at a 25% discount. Discount = ₹600 and SP = ₹1,800.

Finding Discount Percentage and Marked Price

Discount percentage is calculated by dividing the discount amount by the marked price, whereas the marked price can be recovered from SP and the discount rate.

Use Discount% = [(MP − SP)/MP] × 100. If SP and d% are known, MP = SP × 100/(100 − d). For an article sold for ₹720 after a 10% discount, MP = 720 × 100/90 = ₹800.

Example: If MP is ₹1,250 and SP is ₹1,000, discount = ₹250 and discount percentage = 250/1,250 × 100 = 20%.

Successive Discounts

Successive discounts are applied one after another, so the second discount is calculated on the price left after the first discount.

For discounts of a% and b%, the final price is MP × (1 − a/100) × (1 − b/100). The equivalent discount is a + b − ab/100. For 25% and 20%, the net discount is 25 + 20 − 5 = 40%.

Example: On MP ₹1,000, a 25% discount gives ₹750, followed by 20% off ₹750, giving a final SP of ₹600.

Discount with Profit or Loss

Profit or loss is determined by comparing the final selling price with the cost price, even when the article is sold below its marked price.

For p% profit, SP = CP(100 + p)/100. For l% loss, SP = CP(100 − l)/100. If a discount of d% is offered and profit of p% is required, MP = CP(100 + p)/(100 − d).

Example: For CP ₹800, a 15% profit and 20% discount, MP = 800 × 115/80 = ₹1,150.

Difference Between Discount and Profit Percentage

Discount percentage is based on the marked price, while profit percentage is based on the cost price.

Discount% = Discount/MP × 100, but Profit% = Profit/CP × 100. Therefore, equal numerical percentages of discount and profit do not generally refer to equal amounts or the same base.

Example: If CP = ₹600, MP = ₹800 and SP = ₹720, discount = 10% of MP, while profit = ₹120/₹600 × 100 = 20%.

Marked Price and Discount Video Lessons

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6 Lessons
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Successive Discounts and Equivalent Discount

Learn how to calculate the effective discount resulting from successive discounts and convert multiple discounts into an equivalent single discount using standard formulas.

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Practice Marked Price and Discount Questions

Practise published questions related to this topic.

1An article costing Rs. 500 is sold with a Rs. 50 discount. What is the discount percentage?→ 2A person earns 30 percent profit on selling price. What will be his profit percentage on the cost price?→ 3A retailer offers a successive discount of 25% and 15% on a TV set marked at Rs. 80,000. What is the final selling price?→ 4A man bought a laptop for ₹1600 but sold it for ₹1520. Find the percentage loss.→ 5The marked price of an article is 60 percent more than its cost price. What maximum discount percentage can be offered on this article so that there is no loss?→ 6A trader sells an article at a profit of 16%. If he had sold it for ₹80 more, his profit would have been 48%. Find the number of articles sold, given that the total cost price is ₹8,000.→ 7Which of the following will have marked price Rs. 5000?→ 8An item is sold after successive discounts of 30% and 10%. What is the equivalent single discount percentage?→ 9A retailer has fixed the price of an article at 20% above the cost price. If he offers a discount of ₹2 for a purchase of ₹30, what is his gain or loss percentage?→ 10A watch dealer marks the price of a luxury watch 35% above its cost price. During an annual sale, the dealer offers a primary discount of 20% on the marked price. To attract more buyers, a second successive discount of y% is given. If the dealer's overall profit on the transaction is 8% of the cost price, find the value of the second discount y.→

Marked Price and Discount Quick Quiz

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Quick Revision Notes

Marked Price and Discount: Quick Revision

Use these relationships to solve direct, reverse and combined price questions.

  • MP = Discount + SP.
  • Discount% = (Discount/MP) × 100.
  • SP after d% discount = MP(100 − d)/100.
  • MP = SP × 100/(100 − d).
  • Successive discounts a% and b% are equivalent to a + b − ab/100.
  • Profit percentage is calculated on CP, while discount percentage is calculated on MP.
  • For p% profit after d% discount, MP = CP(100 + p)/(100 − d).
  • For l% loss after d% discount, MP = CP(100 − l)/(100 − d).

Marked Price and Discount FAQs

What is the marked price formula when selling price and discount are known?

MP = SP × 100/(100 − discount%). For example, if SP is ₹850 after a 15% discount, MP = 850 × 100/85 = ₹1,000.

How is discount percentage calculated on marked price?

Discount% = [(MP − SP)/MP] × 100. If MP is ₹1,500 and SP is ₹1,200, discount percentage = 300/1,500 × 100 = 20%.

What is the selling price after a 30% discount on ₹2,000?

SP = 2,000 × 70/100 = ₹1,400. The discount amount is ₹600.

Are two successive discounts of 10% and 20% equal to a 30% discount?

No. The net discount is 10 + 20 − (10 × 20)/100 = 28%. The final price is 72% of the marked price.

What marked price gives a 20% profit after a 25% discount when CP is ₹600?

MP = CP × 120/75 = 600 × 120/75 = ₹960. A 25% discount on ₹960 gives SP ₹720, which is 20% above ₹600.

If the marked price is 40% above cost price and a 10% discount is given, what is the profit percentage?

Let CP = ₹100, so MP = ₹140. SP = 90% of ₹140 = ₹126. Profit = ₹26, so profit percentage is 26%.

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