❌ Discount - Common Mistakes to Avoid

🎯 Overview

Discount problems are common in exams but students often make errors in identifying marked price, selling price, and calculating percentages correctly. This guide covers common mistakes and their solutions.

🔥 Critical Mistake Categories

Mistake 1: Wrong Base for Discount Percentage

Common Error:

Calculating discount on selling price instead of marked price

Example:

Question: MP = ₹500, SP = ₹400. Find discount %.

Wrong: Discount % = (100/400) × 100 = 25% ❌ (using SP as base)
Correct: Discount % = (100/500) × 100 = 20% ✅ (using MP as base)

Golden Rule:

• Discount % is ALWAYS calculated on Marked Price (MP)
• Discount = MP - SP
• Discount % = (Discount/MP) × 100

Mistake 2: Confusing MP, CP, and SP

Common Error:

Mixing up marked price, cost price, and selling price

Example:

Question: CP = ₹300, MP = ₹400, Discount = 20%. Find profit %.

Wrong: SP = 400 - 20% = 320, Profit = 320 - 300 = 20, Profit% = 20/300 = 6.67% ❌
Correct: SP = 400 - 20% of 400 = 400 - 80 = 320
Profit = 320 - 300 = 20
Profit% = (20/300) × 100 = 6.67% ✅

Clear Definitions:

• CP: What shopkeeper pays
• MP: Written price tag
• SP: What customer actually pays
• Discount: Reduction from MP

Mistake 3: Successive Discount Errors

Common Error:

Adding successive discounts directly

Example:

Question: MP = ₹1000, discounts 20% and 10%. Find SP.

Wrong: Total discount = 20% + 10% = 30%
SP = 1000 - 30% = 700 ❌

Correct: After 20%: SP = 1000 - 200 = 800
After 10%: SP = 800 - 80 = 720
Equivalent discount = (1000 - 720)/1000 × 100 = 28% ✅

Successive Discount Formula:

Final SP = MP × (1 - d₁/100) × (1 - d₂/100)
Equivalent discount = 1 - (1 - d₁/100) × (1 - d₂/100)

Mistake 4: Discount and Profit Confusion

Common Error:

Not understanding relationship between discount and profit

Example:

Question: CP = ₹200, MP = ₹300, Discount = 25%. Find profit/loss.

Wrong: Discount = 25% of 300 = 75, SP = 300 - 75 = 225
Loss = 225 - 200 = 25, Loss% = 25/225 × 100 = 11.11% ❌

Correct: SP = 300 - 25% of 300 = 300 - 75 = 225
Profit = 225 - 200 = 25
Profit% = (25/200) × 100 = 12.5% ✅

📊 Advanced Concept Mistakes

Mistake 5: Reverse Discount Problems

Common Error:

Wrong calculation when discount percentage is given after profit

Example:

Question: CP = ₹400, Profit = 25%, then discount = 20%. Find SP.

Wrong: Discount on CP = 20% of 400 = 80 ❌
Correct: MP = 400 + 25% = 400 + 100 = 500
SP = 500 - 20% of 500 = 500 - 100 = 400 ✅

Reverse Process Steps:

1. Find MP from CP and profit
2. Apply discount to MP
3. Calculate final SP

Mistake 6: Multiple Items Discount

Common Error:

Applying same discount to all items without checking conditions

Example:

Question: Buy 2 get 1 free, each item MP = ₹100. Find effective discount.

Wrong: Discount = 1/3 = 33.33% ❌
Correct: Pay for 2, get 3 items
Cost = ₹200, Value = ₹300
Discount = (300 - 200)/300 × 100 = 33.33% ✅

Mistake 7: Trade Discount vs Cash Discount

Common Error:

Not distinguishing between trade discount and cash discount

Example:

Question: List price = ₹1000, Trade discount = 20%, Cash discount = 5%. Find payment.

Wrong: Total discount = 25% ❌
Correct: After trade discount: 1000 - 20% = 800
After cash discount: 800 - 5% = 760 ✅

Discount Types:

• Trade Discount: Given on bulk purchases
• Cash Discount: Given for prompt payment
• Sequential: Trade first, then cash

🔢 Complex Scenario Mistakes

Mistake 8: Marked Price Calculation

Common Error:

Wrong calculation when MP needs to be found

Example:

Question: CP = ₹320, Profit = 20%, Discount = 10%. Find MP.

Wrong: MP = 320 + 20% = 384 ❌
Correct: SP = 320 + 20% = 384
Let MP = x
x - 10% of x = 384
0.9x = 384
x = 384/0.9 = 426.67 ✅

Mistake 9: Bill Discount Problems

Common Error:

Wrong calculation in bill discount scenarios

Example:

Question: Bill amount = ₹10000, due in 3 months, discount rate = 12% per annum. Find discount.

Wrong: Discount = 10000 × 12% = 1200 ❌
Correct: Discount = 10000 × 12% × (3/12) = 10000 × 0.12 × 0.25 = 300 ✅

⚡ Quick Verification Methods

Method 1: Logic Check

After discount, SP < MP ✓
After profit, SP > CP ✓
Successive discounts < sum of discounts ✓

Method 2: Range Check

Discount% usually between 5-50% ✓
Profit% usually between 0-50% ✓
Final SP should be reasonable ✓

Method 3: Back Calculation

If MP = 500, discount = 20%, SP = 400
Check: 500 - 20% of 500 = 500 - 100 = 400 ✓

📝 Exam Strategy Tips

Question Approach

1. Identify given values: CP, MP, SP, discount, profit
2. Understand the relationship: What leads to what
3. Apply formulas step by step
4. Calculate carefully
5. Verify with logic

Common Question Patterns

1. Basic discount calculation
2. Successive discounts
3. Discount and profit together
4. Marked price finding
5. Bill discount problems
6. Free item offers

Time Management

• Simple problems: 30-45 seconds
• Medium problems: 60-90 seconds
• Complex problems: 2 minutes maximum

🔗 Related Topics

• - Profit and Loss
• - Percentage calculations
• - Marked Price concepts
• - Successive Discounts

📚 Quick Reference Sheet

Essential Formulas

1. Discount = MP - SP
2. Discount % = (Discount/MP) × 100
3. SP = MP × (1 - Discount%/100)
4. Successive discounts: SP = MP × (1-d₁/100) × (1-d₂/100)
5. Equivalent discount = 1 - (1-d₁/100) × (1-d₂/100)

Quick Calculations

- 10% discount = MP/10 off
- 20% discount = MP/5 off
- 25% discount = MP/4 off
- 50% discount = MP/2 off

Red Flags

• Wrong base for discount percentage
• Adding successive discounts
• Confusing MP, CP, SP
• Wrong sequence in trade/cash discounts
• Calculation errors in percentages

🎯 Next Steps

Master discount problems:

1. Practice basic discount calculations
2. Focus on successive discounts
3. Learn discount-profit combinations
4. Master marked price problems