Commercial Arithmetic: Money – Basic 6 Mathematics Lesson Note (Second Term)

Profit and Loss

Important Terms

• Cost Price (C.P): Amount spent to buy an item
• Selling Price (S.P): Amount received when selling an item
• Profit: When S.P > C.P (you gain money)
• Loss: When C.P > S.P (you lose money)

Formulas

• Profit = S.P – C.P
• Loss = C.P – S.P
• Profit % = (Profit ÷ C.P) × 100
• Loss % = (Loss ÷ C.P) × 100

Examples:

Example 1: Bought a phone for ₦15,000, sold for ₦18,000

• Profit = ₦18,000 – ₦15,000 = ₦3,000
• Profit % = (3,000 ÷ 15,000) × 100 = 20%

Example 2: Bought shoes for ₦8,000, sold for ₦7,200

• Loss = ₦8,000 – ₦7,200 = ₦800
• Loss % = (800 ÷ 8,000) × 100 = 10%

Exercise A – Profit and Loss

Calculate profit/loss and percentage:

1. C.P = ₦5,000, S.P = ₦6,500 Profit/Loss: ₦______ Percentage: ______%
2. C.P = ₦12,000, S.P = ₦10,800 Profit/Loss: ₦______ Percentage: ______%
3. C.P = ₦25,000, S.P = ₦30,000 Profit/Loss: ₦______ Percentage: ______%
4. C.P = ₦18,000, S.P = ₦16,200 Profit/Loss: ₦______ Percentage: ______%
5. C.P = ₦7,500, S.P = ₦9,000 Profit/Loss: ₦______ Percentage: ______%

Simple Interest

Formula

Simple Interest = (Principal × Rate × Time) ÷ 100

Where:

• Principal: Amount borrowed or invested
• Rate: Interest rate per year (%)
• Time: Number of years

Example:

₦10,000 invested at 8% per year for 3 years Simple Interest = (10,000 × 8 × 3) ÷ 100 = ₦2,400 Amount after 3 years = ₦10,000 + ₦2,400 = ₦12,400

Exercise B – Simple Interest

Calculate simple interest and total amount:

1. Principal: ₦5,000, Rate: 6%, Time: 2 years Interest: ₦______ Total Amount: ₦______
2. Principal: ₦15,000, Rate: 10%, Time: 4 years Interest: ₦______ Total Amount: ₦______
3. Principal: ₦8,000, Rate: 5%, Time: 3 years Interest: ₦______ Total Amount: ₦______
4. Principal: ₦20,000, Rate: 7.5%, Time: 2 years Interest: ₦______ Total Amount: ₦______
5. Principal: ₦12,000, Rate: 4%, Time: 5 years Interest: ₦______ Total Amount: ₦______

Discount and Commission

Discount

Discount: Reduction in the marked price of goods

Formulas:

• Discount = Marked Price – Selling Price
• Discount % = (Discount ÷ Marked Price) × 100

Commission

Commission: Payment for selling goods, usually a percentage of sales

Formula:

• Commission = (Commission Rate × Sales) ÷ 100

Examples:

Discount Example: Marked Price = ₦5,000, Discount = 20%

• Discount Amount = (20 ÷ 100) × ₦5,000 = ₦1,000
• Selling Price = ₦5,000 – ₦1,000 = ₦4,000

Commission Example: Sales = ₦50,000, Commission = 5%

• Commission = (5 ÷ 100) × ₦50,000 = ₦2,500

Exercise C – Discount and Commission

Calculate discount and commission:

1. Marked Price: ₦8,000, Discount: 15% Discount Amount: ₦______ Selling Price: ₦______
2. Sales: ₦25,000, Commission Rate: 8% Commission: ₦______
3. Marked Price: ₦12,000, Selling Price: ₦9,600 Discount: ₦______ Discount %: ______%
4. Sales: ₦40,000, Commission Rate: 6% Commission: ₦______
5. Marked Price: ₦15,000, Discount: 25% Discount Amount: ₦______ Selling Price: ₦______

Rate and Tax

Understanding Rates

Rate: Cost per unit (per kg, per liter, per meter, etc.)

Formula:

• Total Cost = Rate × Quantity
• Rate = Total Cost ÷ Quantity

Tax

Tax: Money paid to government, usually a percentage

Common Taxes:

• VAT (Value Added Tax): Usually 7.5% in Nigeria
• Income Tax: Percentage of earnings

Examples:

Rate Example: Rice costs ₦400 per kg

• Cost of 5 kg = ₦400 × 5 = ₦2,000

Tax Example: Income = ₦100,000, Tax = 5%

• Tax Amount = (5 ÷ 100) × ₦100,000 = ₦5,000

Exercise D – Rate and Tax

Calculate using rates and taxes:

1. Petrol costs ₦180 per liter. Find cost of 25 liters Answer: ₦______
2. 12 kg of yam costs ₦3,600. What is the rate per kg? Answer: ₦______ per kg
3. Monthly salary: ₦80,000, Tax: 7.5% Tax Amount: ₦______ Take-home: ₦______
4. Cement costs ₦3,500 per bag. Find cost of 8 bags Answer: ₦______
5. A purchase of ₦15,000 attracts 7.5% VAT VAT Amount: ₦______ Total Cost: ₦______

Share and Dividend

Understanding Shares

Share: Part ownership in a company 

Dividend: Profit paid to shareholders

Key Terms:

• Face Value: Original value of a share
• Market Value: Current price of a share
• Dividend Rate: Percentage of face value paid as dividend

Calculations:

• Number of Shares = Total Investment ÷ Market Price per Share
• Annual Dividend = Number of Shares × Face Value × Dividend Rate ÷ 100

Example:

Tunde buys shares at ₦15 each (face value ₦10) He invests ₦30,000, dividend rate = 8%

• Number of shares = ₦30,000 ÷ ₦15 = 2,000 shares
• Annual dividend = 2,000 × ₦10 × 8 ÷ 100 = ₦1,600

Exercise E – Share and Dividend

Calculate shares and dividends:

1. Investment: ₦50,000, Market Price: ₦25 per share Number of Shares: ______
2. 1,500 shares, Face Value: ₦20, Dividend Rate: 6% Annual Dividend: ₦______
3. Investment: ₦24,000, Market Price: ₦12, Face Value: ₦10, Dividend: 5% Shares: ______ Annual Dividend: ₦______
4. 800 shares, Face Value: ₦50, Dividend Rate: 4% Annual Dividend: ₦______
5. Investment: ₦60,000, Market Price: ₦30, Face Value: ₦25, Dividend: 8% Shares: ______ Annual Dividend: ₦______

Mixed Commercial Problems

Exercise F – Real Life Applications

Solve these business problems:

1. Shop Owner’s Problem: Mama Kemi bought 50 bags of rice at ₦25,000 each. She sold them at ₦28,000 each. What was her total profit and profit percentage? Total Profit: ₦______ Profit %: ______%
2. Bank Investment: Mr. Adebayo invested ₦200,000 in a bank at 12% simple interest for 3 years. How much interest will he earn? Interest: ₦______
3. Sales Agent: A sales agent sold goods worth ₦150,000 and earned 7% commission. How much commission did he receive? Commission: ₦______

Exercise G – Complex Problems

Think and solve:

1. Combined Profit and Loss: A trader bought 20 shirts at ₦1,200 each. He sold 15 at ₦1,500 each and 5 at ₦1,000 each. Did he make profit or loss? How much? Result: ______ Amount: ₦______
2. Discount and VAT: A phone has marked price ₦45,000. After 10% discount, 7.5% VAT is added. What is the final price? Final Price: ₦______
3. Investment Comparison: Which is better: ₦100,000 at 10% simple interest for 2 years, or ₦100,000 at 8% for 3 years? First option interest: ₦______ Second option interest: ₦______ Better option: ______

Exercise H – Mental Calculations

Calculate quickly:

1. 10% profit on ₦5,000 = ₦______
2. 5% commission on ₦20,000 = ₦______
3. 7.5% VAT on ₦8,000 = ₦______
4. Simple interest: ₦1,000 at 10% for 1 year = ₦______
5. 25% discount on ₦12,000 = ₦______

Exercise I – Word Problems

Convert to mathematical problems:

1. Market Problem: A trader sells tomatoes at ₦200 per kg. If she sells 45 kg daily, what is her daily income from tomatoes? Answer: ₦______
2. Salary Problem: A worker earns ₦50,000 monthly. If 15% is deducted as tax and pension, what does he take home? Answer: ₦______
3. Business Partnership: Three friends invest ₦50,000, ₦75,000, and ₦25,000 in a business. If they make ₦30,000 profit, how should it be shared proportionally? First friend: ₦______ Second friend: ₦______ Third friend: ₦______

Answer Key

Exercise A:

1. Profit ₦1,500, 30%
2. Loss ₦1,200, 10%
3. Profit ₦5,000, 20%
4. Loss ₦1,800, 10%
5. Profit ₦1,500, 20%

Exercise B:

1. ₦600, ₦5,600
2. ₦6,000, ₦21,000
3. ₦1,200, ₦9,200
4. ₦3,000, ₦23,000
5. ₦2,400, ₦14,400

Exercise C:

1. ₦1,200, ₦6,800
2. ₦2,000
3. ₦2,400, 20%
4. ₦2,400
5. ₦3,750, ₦11,250

Exercise D:

1. ₦4,500
2. ₦300
3. ₦6,000, ₦74,000
4. ₦28,000
5. ₦1,125, ₦16,125

Exercise E:

1. 2,000
2. ₦1,800
3. 2,000, ₦1,000
4. ₦1,600
5. 2,000, ₦4,000

Exercise F:

1. ₦150,000, 12%
2. ₦72,000
3. ₦10,500

Exercise G:

1. Profit, ₦4,500
2. ₦43,537.50
3. ₦20,000, ₦24,000, Second option

Exercise H:

1. ₦500, 2. ₦1,000, 3. ₦600, 4. ₦100, 5. ₦3,000

Exercise I:

1. ₦9,000
2. ₦42,500
3. ₦10,000, ₦15,000, ₦5,000