Successive Discount: Formula, Rules and Solved Questions

Successive Discount means applying two or more discounts one after another on the reduced price. The second discount is calculated on the price left after the first discount, not on the original marked price. This page explains the net discount formula, equivalent discount, reverse calculations and quick methods with simple numerical examples.

On this page

What Is Successive Discount?

Successive discount is the application of multiple discounts consecutively on the same marked price. Each discount after the first is applied to the price remaining after the previous discount.

For discounts of a% and b%, the final price is Marked Price × (1 − a/100) × (1 − b/100). Therefore, the equivalent single discount is a + b − ab/100 percent. For example, successive discounts of 20% and 10% give a net discount of 20 + 10 − (20 × 10)/100 = 28%.

Successive Discount Formula & Tricks

Important Formulas

Net discount for two discounts
Net discount = a + b − ab/100

If discounts of a% and b% are applied successively, their combined effect is equivalent to one discount of this percentage.

Final selling price for two discounts
SP = MP × (100 − a)/100 × (100 − b)/100

MP is the marked price and SP is the price after both discounts.

Net discount for multiple discounts
Net discount = 100 × [1 − (1 − d₁/100)(1 − d₂/100) ... (1 − dₙ/100)]%

Use this formula when n discounts are applied one after another.

Equal successive discounts
Net discount = 100 × [1 − (1 − d/100)ⁿ]%

Here, d is the equal discount percentage and n is the number of times it is applied.

Quick Tricks

Multiply the remaining percentages

Instead of subtracting each discount separately, retain the price after every discount and multiply the remaining factors. For a discount of d%, the remaining factor is (100 − d)/100.

Example: For 25% and 20% discounts, the remaining factors are 75% and 80%. The final price is 75% × 80% = 60% of MP, so the net discount is 40%.
Do not add successive discounts directly

Adding the percentages gives the wrong result because the second discount applies to the reduced price. For two discounts, subtract the product term ab/100 from their sum.

Example: 20% and 10% are not a 30% discount. Their net discount is 20 + 10 − 2 = 28%.
Use 100 as the assumed marked price

When only discount percentages are given, assume the marked price to be 100. The final price directly gives the remaining percentage, making the net discount easy to calculate.

Example: For 15% and 20%, final price = 100 × 85/100 × 80/100 = 68. The net discount is 32%.

Successive Discount Concepts

Equivalent Single Discount

Multiple successive discounts can be replaced by one equivalent discount calculated from the reduction in the final price.

For discounts a% and b%, the equivalent discount is a + b − ab/100. The result is less than the simple sum of the discounts when both discounts are positive, because the second discount is applied after the first reduction.

Example: For 30% and 20%, equivalent discount = 30 + 20 − (30 × 20)/100 = 44%.

Calculating the Final Selling Price

The final selling price is found by multiplying the marked price by the remaining fraction after each discount.

After a discount of a%, the remaining price is (100 − a)% of the current price. Thus, for a marked price of ₹2,500 and discounts of 20% and 10%, SP = 2,500 × 80/100 × 90/100 = ₹1,800.

Example: The total reduction is ₹2,500 − ₹1,800 = ₹700, so the effective discount is 28%.

Order of Successive Discounts

The order of successive discounts does not affect the final price or the net discount.

Multiplication is commutative: (1 − a/100)(1 − b/100) equals (1 − b/100)(1 − a/100). Therefore, discounts of 20% followed by 10% and 10% followed by 20% both produce a 28% net discount.

Example: On ₹1,000, 20% then 10% gives ₹1,000 × 0.8 × 0.9 = ₹720. Reversing the order also gives ₹720.

Finding the Marked Price from the Final Price

To find the original marked price, divide the final selling price by the product of the remaining discount factors.

If the final price is SP after discounts a% and b%, then MP = SP ÷ [(100 − a)/100 × (100 − b)/100]. For a final price of ₹720 after 20% and 10% discounts, MP = 720 ÷ (0.8 × 0.9) = ₹1,000.

Example: The original price is ₹1,000, because 20% and 10% successive discounts reduce it to ₹720.

Equal Successive Discounts

When the same discount d% is applied n times, the remaining price is MP × (1 − d/100)ⁿ.

The corresponding net discount is 100 × [1 − (1 − d/100)ⁿ]%. For two equal discounts of 10%, the net discount is 100 × (1 − 0.9²) = 19%, not 20%.

Example: On ₹5,000, two successive 10% discounts give ₹5,000 × 0.9 × 0.9 = ₹4,050.

Successive Discount Video Lessons

Watch short topic-wise lessons for quick revision.

6 Lessons
Lesson 1 of 6 Quick Revision

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.

Continue with more lessons and practice in PrepShots.Watch More in App - Start ₹1 Trial →
More Successive Discount Lessons Scroll to explore →

Practice Successive Discount Questions

Practise published questions related to this topic.

1An article is sold for a profit of 50 percent. What is the ratio of the selling price of the article to the cost price of the article?→ 2A grocer marked his goods 80% above the cost price and sold them at a discount of X%. If he made a profit of 8%, find the value of X.→ 3Cost price of an article is Rs. 5000. The loss percentage is 30 percent. What is the selling price of the article?→ 4A shopkeeper sells an item for ₹324.3 after giving two successive discounts of 60% and 31% on its marked price. Had he not given any discount, he would have earned a profit of 25%. What is the cost price (in ₹) of the item?→ 5A sofa set marked at Rs. 78,000 is sold at Rs. 65,000. What is the percentage of discount?→ 6A shopkeeper sells one blender for ₹ 1,000 at a gain of 25% and another for ₹ 1,200 at a loss of 20%. Find his overall profit or loss percentage.→ 7A 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.→ 8A person sells an article at the loss of 30 percent. Cost price and selling price both are decreased by 40 percent. What will be the new loss percentage?→ 9A shopkeeper sells a watch at a loss of 10%. If he had sold it for ₹450 more, he would have made a profit of 5%. What is the cost price of the watch?→ 10During a sale, 50% of the goods are sold at 36% profit, 40% of the remaining goods are sold at 14% profit and the still remaining goods are sold at a loss of 21%. If there is an overall profit of x%, then what is the value of x?→

Successive Discount Quick Quiz

Attempt 5 questions and check your score instantly.

Quick Revision Notes

Successive Discount Revision Points

Use the remaining-price method to handle multiple discounts accurately.

  • For two discounts a% and b%, net discount = a + b − ab/100.
  • Final price = MP × product of all remaining discount factors.
  • A d% discount leaves (100 − d)% of the current price.
  • The order of successive discounts does not change the final price.
  • Successive discounts are not added directly unless the question specifically defines a different basis.
  • For n equal discounts of d%, net discount = 100 × [1 − (1 − d/100)ⁿ]%.
  • To recover MP, divide SP by the product of the remaining factors.

Successive Discount FAQs

What is the successive discount formula for two discounts?

For discounts of a% and b%, net discount = a + b − ab/100%.

What is the net discount for successive discounts of 20% and 10%?

Net discount = 20 + 10 − (20 × 10)/100 = 28%.

What is the final price of an item marked ₹2,000 after 15% and 10% successive discounts?

Final price = 2,000 × 85/100 × 90/100 = ₹1,530.

Are 25% and 15% successive discounts equal to a 40% discount?

No. Their net discount is 25 + 15 − (25 × 15)/100 = 36.25%.

What is the net discount for two successive discounts of 10% each?

Net discount = 10 + 10 − (10 × 10)/100 = 19%.

Does changing the order of successive discounts change the answer?

No. Discounts of a% and b% give the same final price in either order because the remaining factors are multiplied.

Continue learning Successive Discount on PrepShots

Continue on PrepShots