Learning Resources

Money

Interactive curriculum lessons, worked examples, and geometric problem-solving techniques designed to help Kenyan students master CBC, KPSEA, KCSE, and IGCSE mathematics.

Grade 07 Pathway: N/A

First Principles

Objective: Master the core principles of commercial transactions in Kenyan Shillings (KSh): calculating Cost Price, Selling Price, Profit, Loss, Percentage Gain/Loss, Trade Discounts, and Simple Family & Business Budgets.

1. The Foundation: The Money Journey

Every business transaction begins with an investment. When Mama Atieno goes to the wholesale market in Wakulima, Nairobi, she spends money to buy stock. This initial amount spent is the Cost Price (\(CP\)) or Buying Price (\(BP\)).

When she brings her stock to the stall, she sets a price tag known as the Marked Price (\(MP\)). If she sells it directly or gives a customer a price cut (Discount), the final money she receives into her till is the Selling Price (\(SP\)).

2. Visual Bar Model: Profit vs. Loss

Imagine your Cost Price as a solid baseline level:

Profit: When the Selling Price bar is higher than the Cost Price bar, the extra portion earned above the baseline is your Profit (\(SP > CP\)).
Loss: When items are sold below cost (e.g., clearance or perishables), the deficit below the baseline is your Loss (\(CP > SP\)).
Discount: A discount shrinks the Marked Price down to the actual Selling Price. It is calculated as a fraction or percentage of the Marked Price.

3. Fundamental Algebraic Rules

\[\text{Profit} = \text{Selling Price} (SP) - \text{Cost Price} (CP)\]

\[\text{Loss} = \text{Cost Price} (CP) - \text{Selling Price} (SP)\]

\[\%\text{ Profit} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100\%\]

\[\%\text{ Loss} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100\%\]

\[\text{Actual Selling Price} = \text{Marked Price} - \left(\frac{\text{Discount }\%}{100} \times \text{Marked Price}\right)\]

📊 Interactive Market Stall Profit & Loss Simulator

Slide the values below to see how Buying Price, Marked Price, and Customer Discounts interact to create a Profit or a Loss.

Cost Price (Buying Price): KSh 400

Marked Price (Stall Tag): KSh 600

Discount Offered: 10%

Discount Deduction:
KSh 60

Final Selling Price (SP):
KSh 540

Outcome:
Profit of KSh 140

Margin on Cost:
35.0% Profit

Key Formulas

\[\text{Profit} = \text{Selling Price } (SP) - \text{Cost Price } (CP)\]

Occurs when \(SP > CP\). It represents the net financial gain earned after recovering the initial expenditure.

\[\text{Loss} = \text{Cost Price } (CP) - \text{Selling Price } (SP)\]

Occurs when \(CP > SP\). It measures the financial shortfall experienced when an item sells below its total acquisition cost.

\[\text{Percentage Profit} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100\%\]

Crucial Rule: Profit percentage is strictly calculated relative to the original Cost Price (the money invested), never the Selling Price.

\[\text{Percentage Loss} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100\%\]

Relative comparison of financial loss to the base Cost Price invested.

\[\text{Discount Amount} = \frac{\text{Discount }\%}{100} \times \text{Marked Price}\]

The monetary reduction granted to a buyer, computed strictly as a portion of the Marked Price.

\[\text{Actual Selling Price} = \text{Marked Price} - \text{Discount Amount} = \text{Marked Price} \times \left(1 - \frac{\text{Discount }\%}{100}\right)\]

The net amount paid by the customer after subtracting the discount allowance.

\[\text{Total Cost of Stock / Simple Budget} = \sum (\text{Unit Price} \times \text{Quantity}) + \text{Incidental Expenses (Transport, Packing)}\]

A comprehensive budget sums all unit purchasing expenses plus overheads such as boda boda transport or packaging.

Worked Examples

Level 1 (Easy) — Calculating Basic Profit and Percentage Profit:
A poultry farmer in Naivasha buys a crate of eggs from an incubator for KSh 320 and sells it at the roadside kiosk for KSh 400. Calculate:
(a) The profit made.
(b) The percentage profit.

Step 1: Identify given quantities.
Cost Price (\(CP\)) = KSh 320, Selling Price (\(SP\)) = KSh 400.
Step 2: Calculate Profit.
\[\text{Profit} = SP - CP = 400 - 320 = \text{KSh } 80\]
Step 3: Calculate Percentage Profit.
\[\%\text{ Profit} = \left(\frac{\text{Profit}}{CP}\right) \times 100\% = \left(\frac{80}{320}\right) \times 100\% = \frac{1}{4} \times 100\% = 25\%\]
Final Answer: Profit = KSh 80, Percentage Profit = 25%

Level 2 (Medium) — Marked Price, Discount, and Net Gain:
A bookshop in Kisumu displays a mathematics textbook at a marked price of KSh 1,500. The dealer bought the textbook from the publisher at KSh 1,000. During the back-to-school promotion, he offers a 15% discount to parents. Find:
(a) The discount amount given in shillings.
(b) The actual selling price paid by the customer.
(c) The profit made by the bookshop dealer.

Step 1: Calculate the discount amount.
Discount is based on the Marked Price:
\[\text{Discount} = 15\% \text{ of } 1,500 = \frac{15}{100} \times 1,500 = 15 \times 15 = \text{KSh } 225\]
Step 2: Calculate the actual Selling Price.
\[SP = \text{Marked Price} - \text{Discount} = 1,500 - 225 = \text{KSh } 1,275\]
Step 3: Calculate the profit realized.
\[\text{Profit} = SP - CP = 1,275 - 1,000 = \text{KSh } 275\]
Final Answer: Discount = KSh 225, Final Price = KSh 1,275, Profit = KSh 275

Level 3 (Hard) — Multi-Item Budgeting, Overhead Transport, and Profit:
Mama Wanjiku runs a fruit grocery in Eldoret. She plans her weekly budget as follows:

6 sacks of potatoes at KSh 2,500 per sack
4 sacks of onions at KSh 1,800 per sack
Pickup transport from the farm: KSh 1,200

She sells all 6 sacks of potatoes for a total of KSh 18,600. For the onions, she sells 3 sacks at KSh 2,400 each, but the last sack had minor spoilage and was sold at a clearance discount for KSh 1,500. Calculate:
(a) The total expenditure (budget cost).
(b) The total revenue collected.
(c) Her net profit and overall percentage profit.

Step 1: Calculate the total budget cost (including overheads).
\[\text{Potatoes Cost} = 6 \times 2,500 = \text{KSh } 15,000\]\[\text{Onions Cost} = 4 \times 1,800 = \text{KSh } 7,200\]\[\text{Transport} = \text{KSh } 1,200\]\[\text{Total Cost } (CP) = 15,000 + 7,200 + 1,200 = \text{KSh } 23,400\]
Step 2: Calculate the total revenue collected (\(SP\)).
\[\text{Potato Revenue} = \text{KSh } 18,600\]\[\text{Onion Revenue} = (3 \times 2,400) + 1,500 = 7,200 + 1,500 = \text{KSh } 8,700\]\[\text{Total Revenue } (SP) = 18,600 + 8,700 = \text{KSh } 27,300\]
Step 3: Calculate Net Profit and Percentage Profit.
\[\text{Net Profit} = SP - CP = 27,300 - 23,400 = \text{KSh } 3,900\]\[\%\text{ Profit} = \left(\frac{3,900}{23,400}\right) \times 100\% = \left(\frac{1}{6}\right) \times 100\% \approx 16.67\%\]
Final Answer: Total Cost = KSh 23,400, Total Revenue = KSh 27,300, Net Profit = KSh 3,900 (16.67%)

Common Mistakes

Misconception 1: Dividing Profit by Selling Price instead of Cost Price

Mistake If an item bought for KSh 400 is sold for KSh 500 (profit = KSh 100), computing \(\frac{100}{500} \times 100\% = 20\%\).

Correction Profit measures return on investment. Always divide by the Cost Price: \[\%\text{ Profit} = \frac{100}{400} \times 100\% = 25\%\]

Why it feels right The selling price is the most recent cash figure seen at the till, making it tempting to place in the denominator.

Misconception 2: Calculating Discount on Cost Price rather than Marked Price

Mistake Applying a 10% customer discount to the wholesale cost price (e.g., \(10\%\) of KSh 300) rather than the marked shelf price (e.g., KSh 400).

Correction Customers receive discounts off the Marked Price. Cost price is private to the seller.

Why it feels right Both are prices related to the item, so students often confuse which price tag the discount reduces.

Misconception 3: Forgetting Incidental Expenses in Budgeting

Mistake Calculating total cost as only the purchase price of items while ignoring transport (boda boda / matatu fare), market entry fees, or loading charges.

Correction In commercial arithmetic, \(\text{Total Cost Price} = \text{Buying Price} + \text{Incidental Costs}\). Profit is only made if revenue exceeds this total sum.

Why it feels right In everyday conversation, people often quote the price on the receipt and overlook travel costs.

Real World

Retail Kiosk Operations: A shopkeeper buys a 50 kg bale of unga at wholesale price. By factoring in transport, packaging bags, and desired profit margins, she calculates the exact retail selling price per 2 kg packet to remain competitive and profitable.

Boda Boda Transport Business: An operator computes daily fuel costs (KSh 600), bike servicing reserve (KSh 200), and SACCO fees (KSh 100). If total fares collected equal KSh 1,800, his daily net profit is \(1,800 - 900 = \text{KSh } 900\).

End-of-Year School Uniform Discounts: Tailors mark uniforms at KSh 1,200. To attract parents buying multiple sets, they provide a 10% discount on 3 or more sets, creating win-win savings for families while boosting the tailor's bulk sales volume.

Family Monthly Budgeting: Balancing income against prioritized expenditures (school fees, rent, groceries, emergency savings) ensures households avoid deficit spending and build long-term financial security.

Practice

A trader at Gikomba market buys a jacket for KSh 850 and sells it at her stall for KSh 1,200. What is the profit made in Kenyan Shillings? (Type only the number, e.g., 42)

Review the concepts above.

A school bag has a marked price of KSh 1,400 in a supermarket. The store offers a 15% promotional discount. What is the amount of discount given in Kenyan Shillings? (Type only the number, e.g., 42)

Review the concepts above.

A pair of leather shoes has a marked price of KSh 3,200. A shop in Nakuru gives a customer a 10% discount. What is the final selling price paid by the customer in Kenyan Shillings? (Type only the number, e.g., 42)

Review the concepts above.

A carpenter in Machakos made a dining table at a total material cost of KSh 8,000 and sold it for KSh 10,000. What was his percentage profit? (Type only the number, e.g., 25)

Review the concepts above.

Mama Fatuma creates a weekly stock budget for her grocery stall: she buys 5 crates of tomatoes at KSh 1,400 each and 4 sacks of cabbages at KSh 1,100 each. She also pays KSh 600 for pickup transport. She sells all the tomatoes for KSh 9,200 and all the cabbages for KSh 5,800. What is her net profit in Kenyan Shillings? (Type only the number, e.g., 42)

Review the concepts above.

A merchant bought 30 school uniforms at KSh 600 each. He marked each uniform at KSh 900. He sold 20 uniforms at the marked price and the remaining 10 uniforms at a 20% discount. What was his total overall profit in Kenyan Shillings? (Type only the number, e.g., 42)

Review the concepts above.