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JUNIOR SEC β†’ Grade 10 β†’ essential mathematics β†’ Commercial Arithmetic I

Commercial Arithmetic I Notes, Quizzes & Revision

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Essential Mathematics β€” Strand 2.0 Measurements & Geometry

Sub-topic 2.8: Commercial Arithmetic I (age ~15, Kenyan context)

Specific Learning Outcomes
  1. identify and outline the sub-sub-strands: Budget, Discounts and Commission, Profit and Loss, Conversion of different currencies,
  2. prepare budget for use in clubs or societies,
  3. calculate discount and percentage discounts in different situations,
  4. determine commission and percentage commissions in different situations,
  5. determine percentage profit and loss made in the sale of goods,
  6. convert currencies using exchange rate tables,
  7. recognise the role of commercial arithmetic in day-to-day life.
Key concepts & formulae (keep these handy)
  • Budget = plan of expected income and planned expenditure. Balance = Income βˆ’ Total expenditure.
  • Discount amount = Original price Γ— (discount% / 100). Sale price = Original price βˆ’ Discount amount.
  • Commission = Total sales Γ— (commission% / 100). (Often paid to agents or salespeople.)
  • Profit / Loss:
    • Profit = Selling price βˆ’ Cost price (if positive).
    • Loss = Cost price βˆ’ Selling price (if positive).
    • Profit% = (Profit Γ· Cost price) Γ— 100. Loss% = (Loss Γ· Cost price) Γ— 100.
  • Currency conversion:
    • To convert Foreign β†’ KES: Amount Γ— Exchange rate (KES per 1 unit of foreign currency).
    • To convert KES β†’ Foreign: Amount Γ· Exchange rate.
Worked examples (Kenyan context)
Example 1 β€” Preparing a simple club budget
The Drama Club has KSh 5,000 for a performance. Planned items:
  • Refreshments: KSh 2,000
  • Costumes: KSh 1,500
  • Props: KSh 800
  • Posters/printing: KSh 400
Total expenditure = 2,000 + 1,500 + 800 + 400 = KSh 4,700.
Balance = Income βˆ’ Expenditure = 5,000 βˆ’ 4,700 = KSh 300 (leftover). If expenditure > income, plan fundraising or reduce items.
Example 2 β€” Discount
A pair of earphones costs KSh 2,400 with a 15% discount.
Discount amount = 2,400 Γ— 15/100 = 2,400 Γ— 0.15 = KSh 360.
Sale price = 2,400 βˆ’ 360 = KSh 2,040.
Example 3 β€” Commission
A sales agent sells solar lamps worth KSh 45,000 in a month; commission = 6%.
Commission = 45,000 Γ— 6/100 = 45,000 Γ— 0.06 = KSh 2,700.
Example 4 β€” Profit & Loss
A retailer buys a bag of maize flour at KSh 350 and sells at KSh 420.
Profit = 420 βˆ’ 350 = KSh 70.
Profit% = (70 Γ· 350) Γ— 100 = 0.2 Γ— 100 = 20%.

If sold at KSh 320 β†’ Loss = 350 βˆ’ 320 = KSh 30; Loss% = (30 Γ· 350) Γ— 100 β‰ˆ 8.57%.
Example 5 β€” Currency conversion
Exchange table (example rates): 1 USD = KSh 150; 1 GBP = KSh 190; 1 EUR = KSh 165.
Convert US$25 to KSh: 25 Γ— 150 = KSh 3,750.
Convert KSh 5,000 to USD: 5,000 Γ· 150 β‰ˆ US$33.33.
Practice problems
  1. The Chess Club has KSh 6,200. Prepare a budget if they plan: prizes KSh 2,200; snacks KSh 1,900; printing KSh 600; transport KSh 800. How much will remain or is there a deficit?
  2. A shop marks a radio at KSh 8,500 and offers 12% discount. Find the discount amount and sale price.
  3. An agent sells mattresses totaling KSh 120,000 in a quarter. If commission rate is 5%, what is the agent’s commission?
  4. A phone is bought for KSh 9,000 and sold for KSh 10,350. Find profit and profit%.
  5. Using the example rate 1 USD = KSh 150, convert KSh 12,000 to USD. Then convert US$40 to KSh.
  6. Optional challenge: A shop buys 20 boxes of soap at KSh 280 each. If they want a 25% profit on cost, what selling price per box should they set?
Answers (show workings)
  1. Total planned = 2,200 + 1,900 + 600 + 800 = KSh 5,500. Balance = 6,200 βˆ’ 5,500 = KSh 700 (leftover).
  2. Discount = 8,500 Γ— 12/100 = 1,020. Sale price = 8,500 βˆ’ 1,020 = KSh 7,480.
  3. Commission = 120,000 Γ— 5/100 = KSh 6,000.
  4. Profit = 10,350 βˆ’ 9,000 = KSh 1,350. Profit% = (1,350 Γ· 9,000) Γ— 100 = 15%.
  5. KSh β†’ USD: 12,000 Γ· 150 = US$80. USD β†’ KSh: 40 Γ— 150 = KSh 6,000.
  6. Cost per box = KSh 280. Required selling price = cost Γ— (1 + profit%) = 280 Γ— 1.25 = KSh 350 per box.
Suggested learning experiences (fit to Kenyan context, age 15)
  • School-club budgeting: learners prepare a full budget for a class party, sports day or club activity. Include incomes (subscriptions, small fundraisers) and detailed expenditures. Discuss cuts if income is insufficient.
  • Market visit activity: visit a local market (or simulate) to record prices, calculate discounts during sales, compare marked price vs sale price. Use local items (soap, ugali flour, airtime bundles).
  • Role-play sales & commission: set up stalls; some learners act as sales agents earning commission based on sales value. Calculate commissions weekly.
  • Profit & loss shop project: run a small class kiosk for a week (candies, stationery). Record cost price and selling price for items and compute profit or loss and profit%. Reflect on pricing strategy.
  • Currency table exercise: using real exchange rates (check bank/post office rates), convert pocket money from KSh to USD/EUR/GBP and back. Discuss fees and why rates vary.
  • Use spreadsheets or a simple calculator: show how Excel / Google Sheets can help prepare budgets, apply % formulas, and create automatic conversion tables.
  • Project: prepare a one-page simple business plan for a small enterprise (e.g., selling roasted groundnuts). Include budget, expected sales, estimated profit and break-even point.
Teaching & assessment tips
  • Encourage using Kenyan currency (KSh) and local examples to make learning relevant.
  • Assess learners with real-life tasks: prepare budgets, calculate discounts on receipts, compute commission from sales logs.
  • Allow calculators but check understanding by asking for formula explanation and written steps.
  • For stronger learners, add compound problems (e.g., sequential discounts, commission on profit instead of sales, currency conversion with commission/fees).
Note: Exchange rates change frequently β€” always indicate the date and source of any rate used in exercises. Encourage showing all steps when presenting answers.
πŸ“ Practice Quiz

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