Meaning of Commercial Arithmetic

Commercial Arithmetic is the branch of arithmetic that deals with calculations related to trade, business, and commerce.
It involves the mathematical operations used in buying and selling, calculating profits and losses, discounts, commissions, interests, wages, and taxes.
It helps us to manage money, understand financial transactions, and make correct business decisions in commercial activities.

1. It helps to calculate cost price, selling price, profit, and loss.


2. It helps to determine discounts and commissions.


3. It helps to calculate interest on loans, savings, and investments.


4. It helps in determining wages, salaries, and bonuses.


5. It helps in calculating taxes such as VAT and income tax.


6. It helps traders, businessmen, and customers make correct financial decisions.


7. It helps in keeping accurate business records.


8. It helps in comparing prices, costs, and profits.

1. Cost Price (C.P.) – The price at which goods are bought.


2. Selling Price (S.P.) – The price at which goods are sold.


3. Profit – The gain when selling price is greater than cost price.
   
   Profit = S.P. − C.P.


4. Loss – The loss when cost price is greater than selling price.
   Loss = C.P. − S.P.


5. Percentage Profit/Loss
   
   Percentage Profit = (Profit ÷ C.P.) × 100
   
   Percentage Loss = (Loss ÷ C.P.) × 100


6. Discount – A reduction in price to encourage sales.
   
   Discount = (Discount Rate ÷ 100) × Marked Price
   
   Selling Price = Marked Price − Discount


7. Commission – A reward paid to an agent, usually a percentage of total sales.
   
   Commission = (Rate ÷ 100) × Sales


8. Interest
   
   Simple Interest (S.I.) = (Principal × Rate × Time) ÷ 100
   
   Compound Interest (C.I.) = Amount − Principal
   
   Where Amount = Principal × (1 + Rate/100)ᵗ


9. Value Added Tax (VAT)
   
   VAT = (Rate ÷ 100) × Selling Price

1. Profit = S.P. − C.P.


2. Loss = C.P. − S.P.


3. Percentage Profit = (Profit / C.P.) × 100


4. Percentage Loss = (Loss / C.P.) × 100


5. Discount = (Discount Rate / 100) × Marked Price


6. S.P. after Discount = Marked Price − Discount


7. Commission = (Commission Rate / 100) × Total Sales


8. Simple Interest = (P × R × T) / 100


9. Compound Interest = P × (1 + R/100)ᵗ − P


10. VAT = (Rate / 100) × Selling Price

1. Example 1: A trader bought a bag of rice for ₦25,000 and sold it for ₦28,500. Find the profit and percentage profit.
   
   Solution: Profit = ₦28,500 − ₦25,000 = ₦3,500
   
   Percentage Profit = (₦3,500 ÷ ₦25,000) × 100 = 14%
   
   Answer: Profit = ₦3,500; Percentage Profit = 14%.


2. Example 2: A woman bought a dress for ₦12,000 but sold it for ₦10,500. Find the loss and percentage loss.
   
   Solution: Loss = ₦12,000 − ₦10,500 = ₦1,500
   
   Percentage Loss = (₦1,500 ÷ ₦12,000) × 100 = 12.5%
   
   Answer: Loss = ₦1,500; Percentage Loss = 12.5%.


3. Example 3: A trader marks a TV set at ₦80,000 and allows a 10% discount. Find the selling price.
   
   Solution: Discount = (10 ÷ 100) × ₦80,000 = ₦8,000
   
   S.P. = ₦80,000 − ₦8,000 = ₦72,000
   
   Answer: ₦72,000.


4. Example 4: An agent sold goods worth ₦150,000 and received a 5% commission. Find his commission.
   
   Solution: Commission = (5 ÷ 100) × ₦150,000 = ₦7,500
   
   Answer: ₦7,500.


5. Example 5: Find the simple interest on ₦20,000 at 10% per annum for 3 years.
   
   Solution: S.I. = (20,000 × 10 × 3) ÷ 100 = ₦6,000
   
   Answer: ₦6,000.


6. Example 6: Find the compound interest on ₦10,000 at 8% per annum for 2 years.
   
   Solution: Amount = ₦10,000 × (1 + 8/100)² = ₦10,000 × 1.1664 = ₦11,664
   
   C.I. = ₦11,664 − ₦10,000 = ₦1,664
   
   Answer: ₦1,664.


7. Example 7: A trader sells a generator for ₦200,000 including 7.5% VAT. Find the VAT amount.
   
   Solution: VAT = (7.5 ÷ 100) × ₦200,000 = ₦15,000
   
   Answer: ₦15,000.


8. Example 8: A man borrowed ₦50,000 at 6% simple interest for 4 years. How much will he repay?
   
   Solution: S.I. = (50,000 × 6 × 4) ÷ 100 = ₦12,000
   
   Total = ₦50,000 + ₦12,000 = ₦62,000
   
   Answer: ₦62,000.


9. Example 9: A radio has a marked price of ₦15,000 but is sold at 20% discount. Find the selling price.
   
   Solution: Discount = (20 ÷ 100) × ₦15,000 = ₦3,000
   
   S.P. = ₦15,000 − ₦3,000 = ₦12,000
   
   Answer: ₦12,000.


10. Example 10: A trader bought goods for ₦100,000 and sold them at a profit of 25%. Find the selling price.
    
    Solution: Profit = (25 ÷ 100) × ₦100,000 = ₦25,000
    
    S.P. = ₦100,000 + ₦25,000 = ₦125,000
    
    Answer: ₦125,000.


11. Example 11: A loan of ₦40,000 is borrowed at 5% simple interest per year for 2 years. Find the interest and total amount.
    
    Solution: S.I. = (40,000 × 5 × 2) ÷ 100 = ₦4,000
    
    Total = ₦40,000 + ₦4,000 = ₦44,000
    
    Answer: ₦44,000.


12. Example 12: A sales agent earns 7% commission on sales of ₦350,000. Find his commission.
    
    Solution: Commission = (7 ÷ 100) × ₦350,000 = ₦24,500
    
    Answer: ₦24,500.


13. Example 13: A car is sold at ₦1,200,000 with a 5% VAT. Find the VAT and total amount paid.
    
    Solution: VAT = (5 ÷ 100) × ₦1,200,000 = ₦60,000
    
    Total = ₦1,200,000 + ₦60,000 = ₦1,260,000
    
    Answer: ₦1,260,000.


14. Example 14: A trader sold a refrigerator at ₦180,000 and made a 20% profit. Find the cost price.
    
    Solution: S.P. = ₦180,000
    
    Profit = 20% of C.P.
    
    S.P. = C.P. + Profit = C.P. + 0.2C.P. = 1.2C.P.
    
    C.P. = ₦180,000 ÷ 1.2 = ₦150,000
    
    Answer: ₦150,000.


15. Example 15: Find the compound interest on ₦5,000 at 10% per annum for 3 years.
    
    Solution: Amount = ₦5,000 × (1 + 10/100)³ = ₦5,000 × 1.331 = ₦6,655
    
    C.I. = ₦6,655 − ₦5,000 = ₦1,655
    
    Answer: ₦1,655.

1. Buying and selling of goods.


2. Determining profit, loss, and discounts in trade.


3. Calculating interest on loans and savings.


4. Determining VAT and other taxes.


5. Calculating wages, salaries, and commissions.


6. Planning business investments.


7. Comparing market prices and profits.


8. Preparing business budgets and financial records.

1. Using wrong formulas for profit and loss.


2. Forgetting to divide by 100 when converting percentage.


3. Mixing cost price and selling price.


4. Not adding interest to principal when finding amount.


5. Forgetting that discount reduces the selling price.


6. Wrong substitution in formula.

1. A trader bought goods for ₦35,000 and sold them for ₦42,000. Find his profit and percentage profit.


2. A bag of flour is sold for ₦6,000 after a 20% discount. What was the marked price?


3. A loan of ₦50,000 is borrowed at 8% per annum for 2 years. Find the simple interest and total amount.


4. A sales agent sold goods worth ₦250,000 and earned 6% commission. Find his commission.


5. A shopkeeper bought an item for ₦18,000 and sold it at a loss of 15%. Find the selling price.


6. Find the compound interest on ₦15,000 at 10% per annum for 3 years.


7. Calculate the VAT on a generator sold for ₦250,000 at 7.5%.


8. A trader marks a fan at ₦10,000 and allows a 12% discount. Find the selling price.


9. A man bought a radio for ₦4,500 and sold it at a profit of 25%. Find his selling price.


10. A person borrowed ₦80,000 at 9% simple interest for 5 years. Find total amount to be paid.

Conclusion

Commercial Arithmetic is very important in business and daily financial life.
It helps us to calculate profits, losses, discounts, and interests correctly.
It helps us to make good business decisions, manage money wisely, and ensure financial success.