🚫 Profit and Loss - Common Mistakes to Avoid

Master profit and loss calculations by understanding and avoiding these common pitfalls that cost marks in IBPS exams.

🔍 Most Common Mistakes

1. Wrong Base for Percentage Calculation

Mistake: Using Selling Price instead of Cost Price

Problem: CP = ₹200, SP = ₹250. Find profit percentage.

❌ Wrong Approach:
Profit % = (50/250) × 100 = 20%

✓ Correct Approach:
Profit % = (50/200) × 100 = 25%

Practice Question:

A shopkeeper buys an article for ₹800 and sells it for ₹960. Find the profit percentage.

Solution:

• Profit = 960 - 800 = ₹160
• Profit % = (160/800) × 100 = 20%

2. Cost Price, Selling Price, Marked Price Confusion

Mistake: Confusing between CP, SP, and MP

Problem: Marked Price = ₹500, Discount = 20%, Profit = 10%. Find CP.

❌ Wrong Approach:
SP = 500 - 20% = 400
CP = 400 - 10% = 360

✓ Correct Approach:
SP = 500 - 20% of 500 = 500 - 100 = 400
Since profit is 10% on CP: SP = CP × 1.1
400 = CP × 1.1
CP = 400/1.1 = ₹363.64

Practice Question:

An article is marked at ₹1,200. The shopkeeper offers a discount of 25% and still makes a profit of 20%. Find the cost price.

Solution:

• SP = 1200 - 25% of 1200 = 1200 - 300 = ₹900
• Since profit = 20% on CP: SP = CP × 1.2
• 900 = CP × 1.2
• CP = 900/1.2 = ₹750

3. Successive Discounts and Profits

Mistake: Adding percentages directly

Problem: Successive discounts of 20% and 10%.

❌ Wrong Approach:
Total discount = 20% + 10% = 30%

✓ Correct Approach:
Equivalent discount = 1 - (0.8 × 0.9) = 1 - 0.72 = 28%

Practice Question:

A shopkeeper offers two successive discounts of 15% and 10%. What is the equivalent single discount?

Solution:

• Equivalent discount = 1 - (0.85 × 0.9) = 1 - 0.765 = 23.5%

4. Dishonest Dealer Problems

Mistake: Not understanding false weights

Problem: Dealer claims to sell 1kg at ₹50 but gives only 900g. Actual CP per kg = ₹40. Find profit %.

❌ Wrong Approach:
Profit = 50 - 40 = ₹10
Profit % = (10/40) × 100 = 25%

✓ Correct Approach:
CP for 900g = 40 × 0.9 = ₹36
SP for 900g = ₹50
Profit = 50 - 36 = ₹14
Profit % = (14/36) × 100 = 38.89%

Practice Question:

A shopkeeper uses a false weight of 800g for 1kg and sells at cost price. What is his profit percentage?

Solution:

• Let CP per kg = ₹100
• CP for 800g = ₹80
• SP for 800g (selling as 1kg at CP) = ₹100
• Profit = 100 - 80 = ₹20
• Profit % = (20/80) × 100 = 25%

5. Discount Percentage Errors

Mistake: Wrong base for discount calculation

Problem: MP = ₹400, SP = ₹340. Find discount %.

❌ Wrong Approach:
Discount % = (400-340)/340 × 100 = 17.65%

✓ Correct Approach:
Discount % = (400-340)/400 × 100 = 15%

Practice Question:

The marked price of an article is ₹250 and the selling price is ₹200. Find the discount percentage.

Solution:

• Discount = 250 - 200 = ₹50
• Discount % = (50/250) × 100 = 20%

6. Loss Percentage Calculation Errors

Mistake: Using SP as base for loss percentage

Problem: CP = ₹500, SP = ₹400. Find loss %.

❌ Wrong Approach:
Loss % = (100/400) × 100 = 25%

✓ Correct Approach:
Loss % = (100/500) × 100 = 20%

Practice Question:

A trader sells an article for ₹320 at a loss of 20%. Find the cost price.

Solution:

• SP = CP × (1 - Loss%)
• 320 = CP × 0.8
• CP = 320/0.8 = ₹400

7. Mixed Transaction Problems

Mistake: Wrong order of operations

Problem: CP = ₹100, first 20% profit, then 10% discount on SP.

❌ Wrong Approach:
Net effect = 20% - 10% = 10% profit

✓ Correct Approach:
SP after profit = 100 × 1.2 = ₹120
Final SP after discount = 120 × 0.9 = ₹108
Net profit = 8%

Practice Question:

A shopkeeper first marks up the price by 50% and then gives a discount of 20%. Find the overall profit percentage.

Solution:

• Let CP = ₹100
• MP = 100 × 1.5 = ₹150
• SP = 150 × 0.8 = ₹120
• Profit = 120 - 100 = ₹20
• Profit % = 20%

8. Partnership Business Errors

Mistake: Wrong profit sharing ratio

Problem: A invests ₹2000 for 6 months, B invests ₹3000 for 4 months. Total profit = ₹2200.

❌ Wrong Approach:
A's share = (2000/5000) × 2200 = ₹880

✓ Correct Approach:
A's capital months = 2000 × 6 = 12000
B's capital months = 3000 × 4 = 12000
Ratio = 1:1, so A's share = ₹1100

Practice Question:

A and B invest ₹25,000 and ₹15,000 respectively in a business. If A invested for 8 months and B for 6 months, and the total profit is ₹4,200, find A’s share.

Solution:

• A’s capital months = 25000 × 8 = 200,000
• B’s capital months = 15000 × 6 = 90,000
• Ratio = 200,000 : 90,000 = 20:9
• Total parts = 29
• A’s share = (20/29) × 4200 = ₹2,896.55

9. Average Cost Calculation Errors

Mistake: Simple average instead of weighted average

Problem: 50 apples at ₹4 each, 30 apples at ₹6 each. Find average cost.

❌ Wrong Approach:
Average = (4 + 6)/2 = ₹5

✓ Correct Approach:
Total cost = (50 × 4) + (30 × 6) = 200 + 180 = ₹380
Total apples = 80
Average cost = 380/80 = ₹4.75

Practice Question:

A shopkeeper bought 100 pens at ₹10 each and 150 pens at ₹8 each. Find the average cost per pen.

Solution:

• Total cost = (100 × 10) + (150 × 8) = 1000 + 1200 = ₹2,200
• Total pens = 100 + 150 = 250
• Average cost = 2200/250 = ₹8.80

10. Break-Even Point Mistakes

Mistake: Ignoring fixed costs

Problem: Fixed cost = ₹1,000, Variable cost per unit = ₹10, SP per unit = ₹15. Find break-even quantity.

❌ Wrong Approach:
Set SP = VC, so 15 = 10

✓ Correct Approach:
Total Cost = Fixed + (Variable × Quantity)
Total Revenue = SP × Quantity
At break-even: 1000 + 10Q = 15Q
5Q = 1000, Q = 200 units

Practice Question:

A company has fixed costs of ₹50,000 and variable cost of ₹20 per unit. If the selling price is ₹30 per unit, find the break-even point.

Solution:

• Let Q be the break-even quantity
• Total Cost = 50,000 + 20Q
• Total Revenue = 30Q
• At break-even: 50,000 + 20Q = 30Q
• 10Q = 50,000
• Q = 5,000 units

🎯 Special Cases and Advanced Mistakes

11. Tax and GST Problems

Mistake: Not including tax in final price

Problem: CP = ₹1000, GST = 18%, Profit margin = 20% on CP. Find SP including tax.

❌ Wrong Approach:
SP = 1000 + 20% = ₹1200

✓ Correct Approach:
Base SP = 1000 + 20% of 1000 = ₹1200
Final SP = 1200 + 18% GST = ₹1416

12. Multi-Stage Transaction Problems

Mistake: Not tracking costs through multiple transactions

Problem: Bought at ₹200, sold at ₹250 at 10% commission, bought back at ₹300 with 5% commission.

❌ Wrong Approach:
Simple profit/loss calculation

✓ Correct Approach:
Track all costs and revenues including commissions

📝 Practice Questions to Avoid Mistakes

Set 1: Basic Profit/Loss

1. CP = ₹450, SP = ₹540. Find profit %
2. CP = ₹800, SP = ₹720. Find loss %
3. Profit = ₹120, Profit % = 15%. Find CP

Set 2: Discount Problems

4. MP = ₹300, Discount = 25%. Find SP
5. SP = ₹480, Discount % = 20%. Find MP
6. MP = ₹600, SP = ₹450. Find discount %

Set 3: Successive Transactions

7. CP = ₹200, 25% profit, then 10% discount. Find SP
8. Two successive discounts of 20% and 15%. Find equivalent discount
9. Markup 30%, then discount 20%. Find profit/loss %

Set 4: Complex Problems

10. False weight: Sells 900g as 1kg, CP/kg = ₹40, SP/kg = ₹60. Find profit %
11. Partnership: A invests ₹20,000 for 8 months, B invests ₹30,000 for 6 months. Total profit = ₹4,800. Find A’s share
12. Break-even: Fixed cost = ₹20,000, VC = ₹5/unit, SP = ₹8/unit. Find break-even quantity

🎯 Quick Tips to Avoid Mistakes

Memory Rules:

1. Profit/Loss % always on CP - never on SP
2. Discount % always on MP - never on SP
3. False weight profit = (Error in both buying and selling)
4. Successive operations = Multiply factors, don’t add percentages

Calculation Tips:

1. Write variables clearly - CP, SP, MP
2. Use formulas systematically - don’t mix them up
3. Check reasonableness - profit should usually be < 100%
4. Verify with reverse calculation - check your answer

Common Formulas:

• Profit = SP - CP
• Loss = CP - SP
• Profit % = (Profit/CP) × 100
• Loss % = (Loss/CP) × 100
• SP = CP × (1 + Profit%/100)
• Discount = MP - SP

🔗 Related Topics

📚 Quick Formula Reference

• Profit: SP - CP
• Loss: CP - SP
• Profit %: (Profit/CP) × 100
• Loss %: (Loss/CP) × 100
• SP when profit% known: CP × (1 + Profit%/100)
• SP when loss% known: CP × (1 - Loss%/100)
• Discount: MP - SP
• Discount %: (Discount/MP) × 100

Remember: Always identify what the percentage is calculated on - CP for profit/loss, MP for discount.