Profit and Loss

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Profit and Loss — Key Facts for NABE (Pakistan)

• Cost Price (CP): Price at which an article is bought
• Selling Price (SP): Price at which an article is sold
• Profit/Loss: SP > CP = Profit; SP < CP = Loss
• Profit % = (Profit/CP) × 100 | Loss % = (Loss/CP) × 100
• SP = CP × (1 + Profit%/100) | SP = CP × (1 - Loss%/100)
• ⚡ Exam tip: Always calculate percentage based on Cost Price, not Selling Price

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Profit and Loss — NABE (Pakistan) Study Guide

Basic Terminology

• Cost Price (CP): The actual amount paid to purchase an item (includes all expenses)
• Selling Price (SP): The amount received from selling an item
• Profit/Gain: When SP > CP → Profit = SP - CP
• Loss: When CP > SP → Loss = CP - SP
• Overhead Expenses: Additional costs like transportation, packaging, etc. are added to CP

Key Formulas

Profit/Loss Calculations:

Profit = SP - CP (when SP > CP)
Loss = CP - SP (when CP > SP)

Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100

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

CP = SP / (1 + Profit%/100)
CP = SP / (1 - Loss%/100)

Important Examples

Example 1: A shopkeeper buys a shirt for Rs. 400 and sells it for Rs. 500.

• CP = 400, SP = 500
• Profit = 500 - 400 = Rs. 100
• Profit % = (100/400) × 100 = 25%

Example 2: A fruit seller buys 20 kg of apples at Rs. 50/kg and 5 kg spoil. He sells the remaining at Rs. 70/kg. Find profit %.

• Total CP = 20 × 50 = Rs. 1000
• Sold quantity = 15 kg at Rs. 70/kg = Rs. 1050
• Profit = 1050 - 1000 = Rs. 50
• Profit % = (50/1000) × 100 = 5%

Discount

Formula:

Discount = Marked Price (MP) - Selling Price (SP)
Discount % = (Discount/MP) × 100

Note: Discount is always calculated on the Marked Price, not Cost Price.

Break-Even Point

When SP = CP (no profit, no loss):

Profit/Loss = Rs. 0

NABE Exam Pattern

Common question types:

1. Direct profit/loss calculations
2. Finding SP or CP when profit/loss percentage is given
3. Discount and marked price problems
4. Dishonest merchant problems (selling at wrong weight)
5. Successive transactions

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Profit and Loss — Comprehensive NABE (Pakistan) Notes

Detailed Theory

1. Cost Price Components

True Cost Price includes:

• Purchase price of goods
• Freight/transportation costs
• Packaging charges
• Insurance during transit
• Loading and unloading charges
• Custom duty (if imported)
• Storage costs

Example: A trader buys goods worth Rs. 10,000. He pays Rs. 500 for transport and Rs. 200 for packaging. Find actual CP.

• Actual CP = 10,000 + 500 + 200 = Rs. 10,700

2. Selling Price Considerations

True SP excludes:

• Any return of goods
• Any commission paid to agents

3. Percentage Calculations — Critical Rules

Golden Rule: Profit percentage and Loss percentage are ALWAYS calculated on Cost Price, NEVER on Selling Price.

Verification:

• Buy at Rs. 80, sell at Rs. 100
• Profit = 20, Profit % = 20/80 × 100 = 25%
• NOT 20/100 × 100 = 20% (incorrect!)

Loss Percentage is also always on CP:

• Buy at Rs. 120, sell at Rs. 100
• Loss = 20, Loss % = 20/120 × 100 = 16.67%

4. Interchanging SP and CP

Problem: Find profit % when SP of an article is Rs. 120 and profit equals cost price of 2 articles.

Let CP of 1 article = x

• Profit = CP of 2 articles = 2x
• SP = CP + Profit = x + 2x = 3x = 120
• x = 40
• CP = 40, Profit = 80
• Profit % = (80/40) × 100 = 200%

5. Successive Selling

Problem: A merchant sells at profit of 20%. If the buyer sells at Rs. 180 and makes 25% profit, find original cost.

• Let original CP = x
• First merchant sells at = 1.2x
• Second merchant buys at = 1.2x
• Second merchant’s SP = 1.2x × 1.25 = 180
• 1.5x = 180
• x = Rs. 120

6. Discount Problems

Types of Discount:

• Trade Discount: Given by wholesaler to retailer (percentage on MP)
• Cash Discount: Given for quick payment (percentage on invoice price)
• Successive Discounts: Multiple discounts applied one after another

Successive Discount Formula: If discounts are d₁%, d₂%, d₃%:

Final Price = MP × (1 - d₁/100) × (1 - d₂/100) × (1 - d₃/100)

Example: MP = Rs. 1000, successive discounts 20% and 10%

• After 20% discount: 1000 × 0.8 = Rs. 800
• After 10% discount: 800 × 0.9 = Rs. 720
• NOT 1000 × 0.7 = Rs. 700!

Equivalent Single Discount:

• Two successive discounts of 20% and 10% = Equivalent single discount of 28%
• Formula: d_eq = d₁ + d₂ - (d₁ × d₂)/100

7. Dishonest Merchant Problems

Selling at Wrong Weight:

• Gain% = [(True Weight - False Weight) / False Weight] × 100

Example: A shopkeeper uses a false weight of 900g for 1kg. Find his gain %.

• Claims to sell 1000g but gives only 900g
• Gain = 1000 - 900 = 100g on 900g
• Gain % = (100/900) × 100 = 11.11%

Selling at Cost Price with False Weight:

• Gain% = (Error / (Measured - Error)) × 100

8. Marked Price vs. Cost Price

Markup (on CP) vs. Discount (on MP):

• If MP = CP and markup = m%, discount = m%
• Then SP = CP (break-even, not profit!)

Problem: If cost price is Rs. 300 and profit required is 20%, what should be the selling price?

• Required SP = 300 × 1.20 = Rs. 360

Problem: If cost price is Rs. 300 and profit required is 20%, but we offer 10% discount on MP. What should MP be?

• Required SP = 360
• 360 = MP × 0.90
• MP = Rs. 400

9. Combined Transactions

Problem: A man buys 2 horses at Rs. 500 each. He sells one at 10% profit and another at 10% loss. Find overall transaction result.

• Total CP = 500 + 500 = 1000
• First SP = 500 × 1.10 = 550
• Second SP = 500 × 0.90 = 450
• Total SP = 550 + 450 = 1000
• Overall = No profit, no loss!

Key Insight: Equal profit% and equal loss% on equal CP = No profit no loss overall.

10. Common Mistakes to Avoid

1. Wrong Base: Always use CP as the base for percentage calculations
2. Ignoring Overhead Costs: Always add transportation, packaging, etc. to CP
3. Discount Confusion: Discount is on MP, not on CP
4. Successive Operations: Be careful with successive profit/loss calculations
5. Unit Consistency: Ensure all units are consistent

Practice Questions for NABE

1. A shopkeeper buys an article for Rs. 800 and wants a profit of 20%. At what price should he sell?
2. Two articles are sold at Rs. 600 each. One is sold at 20% profit and the other at 20% loss. Find overall profit/loss.
3. The marked price of an article is Rs. 5000. It is sold at two successive discounts of 20% and 10%. Find the selling price.
4. A shopkeeper makes a profit of 25% by selling a fan for Rs. 1250. Find the cost price.
5. A trader sells goods at cost price but uses 800g weight instead of 1kg. Find his profit percentage.

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