Discount - All Formulas & Shortcuts

Quick reference guide for all Discount formulas with instant solving techniques

📘 Basic Definitions

1. Key Terms

Marked Price (MP) = List Price = The price tag on product Selling Price (SP) = Actual price paid by customer Cost Price (CP) = Price at which seller bought the item Discount = Reduction from Marked Price

Relationship:

SP = MP - Discount Discount% = (Discount/MP) × 100

2. Fundamental Formulas

Discount calculation:

Discount = MP - SP Discount% = [(MP - SP)/MP] × 100

Finding SP from discount:

SP = MP × (100 - Discount%)/100 SP = MP × (1 - Discount%/100)

Finding MP from SP:

MP = SP × 100/(100 - Discount%) MP = SP/(1 - Discount%/100)

⚡ Quick Shortcuts

3. Single Discount Shortcuts

If discount is x%:

SP = MP × (100-x)/100

Quick calculation:

• 10% discount: SP = MP × 0.9
• 20% discount: SP = MP × 0.8
• 25% discount: SP = MP × 0.75
• 30% discount: SP = MP × 0.7
• 50% discount: SP = MP × 0.5

Example: MP = 1000, 20% discount

SP = 1000 × 0.8 = 800

4. Successive Discounts (MOST IMPORTANT!)

Two successive discounts of x% and y%:

Formula:

Net Discount% = x + y - (xy/100)

Effective SP = MP × [(100-x)/100] × [(100-y)/100]

Example: MP = 2000, discounts 20% and 10%

Method 1 (Net Discount): Net Discount = 20 + 10 - (20×10)/100 = 30 - 2 = 28% SP = 2000 × 72/100 = 1440

Method 2 (Successive): After 20%: 2000 × 0.8 = 1600 After 10%: 1600 × 0.9 = 1440

5. Three Successive Discounts

Discounts of a%, b%, and c%:

Formula:

SP = MP × [(100-a)/100] × [(100-b)/100] × [(100-c)/100]

Net Discount:

Net% = a + b + c - (ab+bc+ac)/100 + abc/10000

Example: 20%, 15%, 10% on MP = 5000

SP = 5000 × 0.8 × 0.85 × 0.9 = 3060

Net Discount = 20 + 15 + 10 - (300+150+200)/100 + (20×15×10)/10000 = 45 - 6.5 + 0.3 = 38.8%

💡 Advanced Formulas

6. Discount with Profit/Loss

When both discount and profit are involved:

MP related to CP:

MP = CP × (100 + Markup%)/100

If profit is p% and discount is d%: SP = CP × (100+p)/100 SP = MP × (100-d)/100

Therefore: CP × (100+p)/100 = MP × (100-d)/100

Example: CP = 800, 25% markup, 10% discount

MP = 800 × 1.25 = 1000 SP = 1000 × 0.9 = 900 Profit = 900 - 800 = 100 (12.5% profit)

7. Finding Markup% Given Discount and Profit

If discount is d% and profit is p%:

Formula:

Markup% = [(100+p)/(100-d) - 1] × 100

OR

MP/CP = (100+p)/(100-d)

Example: Profit 20%, Discount 10%, find Markup%

Markup% = [(100+20)/(100-10) - 1] × 100 = [120/90 - 1] × 100 = [1.333 - 1] × 100 = 33.33%

8. Two Items with Same Discount%

If discount% is same on both items:

Average SP = Average MP × (100-Discount%)/100

Important Pattern: If same discount% on two different MPs:

• Discount amounts are proportional to MPs
• SPs are also proportional to MPs

🔥 Exam Patterns

9. Pattern 1: MP is x% more than CP

MP = CP + x% of CP:

MP = CP × (100+x)/100

If discount is d%, find profit%:

SP = MP × (100-d)/100 = CP × (100+x)/100 × (100-d)/100

Profit% = [(100+x)(100-d)/10000 - 1] × 100

Example: MP is 40% more than CP, discount 20%

Profit% = [140 × 80/10000 - 1] × 100 = [1.12 - 1] × 100 = 12%

10. Pattern 2: Equal Successive Discounts

Two equal discounts of x% each:

Net Discount:

Net% = x + x - x²/100 = 2x - x²/100

Shortcut: Net% = x(2 - x/100)

Example: Two successive 10% discounts

Net = 10(2 - 10/100) = 10(1.9) = 19%

Common Equal Discounts:

• 10% + 10% = 19%
• 20% + 20% = 36%
• 25% + 25% = 43.75%
• 30% + 30% = 51%

11. Pattern 3: Discount Series Problems

If discounts d₁%, d₂%, d₃% are given in sequence:

Always multiply remaining percentages:

Final % of MP = (100-d₁)/100 × (100-d₂)/100 × (100-d₃)/100

Never add discounts directly! ❌ Wrong: 20% + 30% = 50% ✅ Correct: 0.8 × 0.7 = 0.56 = 44% discount

🎯 Special Cases

12. False Discount Problems

Shopkeeper claims discount but gives less:

Actual Discount:

If claims x% but gives y% worth: True Discount = 100 - [(100-y)/(100-x) × 100]

Example: Claims 20% but weighs 900g for 1kg

Effective discount = 100 - (90/80 × 100) = 100 - 112.5 = -12.5% (Actually 12.5% profit!)

13. Cashback as Discount

Cashback of x% on SP:

Effective Discount from MP:

If SP = MP(1-d₁) and cashback is c% of SP:

Effective price = SP(1-c/100) = MP(1-d₁)(1-c/100)

Net Discount% = [1 - (1-d₁)(1-c/100)] × 100

Example: 20% discount + 10% cashback on MP = 1000

SP = 800 Cashback = 80 Effective = 720 Net Discount = 28%

💎 Mental Math Tricks

Trick 1: Quick Successive Discounts

For 10% + 20%:

After 10%: 90% remains After 20%: 80% of 90% = 72% Discount = 28%

For 20% + 25%:

After 20%: 80% remains After 25%: 75% of 80% = 60% Discount = 40%

Trick 2: Finding Third Discount

If two discounts give x% net, find equivalent single discount:

Given: d₁% and d₂%

Single equivalent = d₁ + d₂ - (d₁ × d₂)/100

Example: 30% then 20% = ?

= 30 + 20 - 600/100 = 44%

Trick 3: Discount to SP Conversion

Memorize multipliers:

10% off → × 0.90 15% off → × 0.85 20% off → × 0.80 25% off → × 0.75 30% off → × 0.70 33⅓% off → × 0.667 (⅔) 40% off → × 0.60 50% off → × 0.50

Trick 4: Finding Original Price

SP is x% less than MP:

If SP = 600 and discount is 25%: MP = 600/(1-0.25) = 600/0.75 = 800

Quick division:

• 10% off: Divide by 0.9
• 20% off: Divide by 0.8
• 25% off: Divide by 0.75 (= multiply by 4/3)
• 50% off: Multiply by 2

📊 Formula Summary

Scenario	Formula
Basic Discount	SP = MP - Discount
Discount%	(Discount/MP) × 100
SP from Discount%	MP × (100-d)/100
Two Discounts	Net% = d₁ + d₂ - d₁d₂/100
Three Discounts	Multiply: (100-d₁)(100-d₂)(100-d₃)/10000
MP from CP	CP × (100+markup)/100
Profit with Discount	CP(100+p)/100 = MP(100-d)/100

🔍 Common Mistakes

❌ Adding successive discounts: 20% + 30% ≠ 50% ❌ Calculating discount on SP instead of MP ❌ Confusing Markup% with Profit% ❌ Using SP as base instead of MP for discount% ✅ Always apply successive discounts one by one ✅ Discount is always on Marked Price (MP) ✅ Markup is on CP, Discount is on MP ✅ Remember: SP = MP × (1 - Discount%)

🎓 Solved Examples

Example 1: Basic Successive Discount

Q: MP = 2500. Discounts: 20% and 16%. Find SP.

Solution:

Method 1 (Net %): Net = 20 + 16 - (20×16)/100 = 36 - 3.2 = 32.8% SP = 2500 × 67.2/100 = 1680

Method 2 (Successive): After 20%: 2500 × 0.8 = 2000 After 16%: 2000 × 0.84 = 1680

Example 2: Finding Markup

Q: CP = 1200, Profit = 20%, Discount = 25%. Find MP.

Solution:

SP = 1200 × 1.20 = 1440 SP = MP × 0.75 1440 = MP × 0.75 MP = 1440/0.75 = 1920

Markup = 1920 - 1200 = 720 Markup% = 720/1200 × 100 = 60%

Example 3: Three Discounts

Q: MP = 10000. Discounts: 10%, 20%, 30%. Find final SP.

Solution:

After 10%: 10000 × 0.9 = 9000 After 20%: 9000 × 0.8 = 7200 After 30%: 7200 × 0.7 = 5040

OR direct: SP = 10000 × 0.9 × 0.8 × 0.7 = 5040

🔗 Related Resources

Practice Questions:

• Discount Practice Questions

Theory:

• Discount Theory & Concepts

Related Topics:

• Profit & Loss
• Percentage
• Ratio & Proportion

Study Resources:

• All-in-One Formula Sheet

Master successive discounts and you’ll solve any discount problem! ⚡

Remember: Never add successive discounts - always multiply! 🚀