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Percentages (applications: profit, loss, discount, commission) — KCSE Mathematics

KCSE Mathematics · 97 practice questions · 4 syllabus objectives · 4 revision lessons

31 easy31 medium35 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Express a quantity as a percentage of another and calculate percentage increase and decrease

Calculate profit, loss, discount and commission as percentages and apply to buying and selling scenarios

Solve problems involving taxation (VAT, income tax), insurance premiums and percentage error in measurement

Percentages (applications: profit, loss, discount, commission)

Revision Notes

Concise lesson notes for Percentages (applications: profit, loss, discount, commission), written to the KCSE Mathematics marking standard. Read the first lesson free below.

Understanding Percentages: Increase and Decrease

To express a quantity as a percentage of another, use the formula:
Percentage = (Part/Whole) × 100.
For example, if you have 20 apples out of 50, the percentage is:
(20/50) × 100 = 40%.

To calculate percentage increase, use:
Percentage Increase = [(New Value - Original Value) / Original Value] × 100.
For instance, if a price rises from Ksh 200 to Ksh 250:
Percentage Increase = [(250 - 200) / 200] × 100 = 25%.

Conversely, for percentage decrease:
Percentage Decrease = [(Original Value - New Value) / Original Value] × 100.
If a price drops from Ksh 300 to Ksh 240:
Percentage Decrease = [(300 - 240) / 300] × 100 = 20%.

Understanding these concepts is crucial for solving real-life problems involving finances.

Key points to remember

  • Percentage = (Part/Whole) × 100 for expressing quantities.
  • Percentage Increase = [(New - Original) / Original] × 100.
  • Percentage Decrease = [(Original - New) / Original] × 100.
  • Use clear values to calculate percentage changes.
  • Mastering percentages aids in financial literacy.

Worked example

If a shirt costs Ksh 800 and is sold for Ksh 600, calculate the percentage decrease.
Percentage Decrease = [(800 - 600) / 800] × 100 = 25%.

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More lessons in this topic

Lesson 2: Calculating Profit, Loss, Discount, and Commission

Objective: Calculate profit, loss, discount and commission as percentages and apply to buying and selling scenarios

In business transactions, it is essential to understand how to calculate profit, loss, discount, and commission as percentages. Profit is the amount earned above the cost price (CP), while loss is the amount lost when the selling price (SP) is less than the CP.

To find profit or loss percentage:

  • Profit Percentage = (Profit / CP) × 100
  • Loss Percentage = (Loss / CP) × 100

Discount is a reduction from the marked price (MP) of an item. The discount percentage is calculated as:

  • Discount Percentage = (Discount / MP) × 100

Commission is a fee paid to an agent based on sales. To calculate commission percentage:

  • Commission Percentage = (Commission / Selling Price) × 100

Example 1: If an item costs Ksh 100 and sells for Ksh 120, the profit is Ksh 20.

  • Profit Percentage = (20 / 100) × 100 = 20%.

Example 2: If a shop offers a 10% discount on a Ksh 200 item, the discount amount is Ksh 20.

  • Discount Percentage = (20 / 200) × 100 = 10%.
  • Profit = Selling Price - Cost Price.
  • Loss = Cost Price - Selling Price.
  • Discount = Marked Price - Selling Price.
  • Commission = Percentage of total sales.
  • Always express profit, loss, discount, and commission as percentages.

A laptop costs Ksh 80,000 and is sold for Ksh 100,000. Calculate the profit percentage.

  • Profit = 100,000 - 80,000 = Ksh 20,000.
  • Profit Percentage = (20,000 / 80,000) × 100 = 25%.
Lesson 3: Understanding Taxation and Percentage Errors

Objective: Solve problems involving taxation (VAT, income tax), insurance premiums and percentage error in measurement

In this lesson, we will solve problems involving taxation and percentage errors. Taxation includes VAT (Value Added Tax) and income tax. To calculate VAT, use the formula:

  • VAT Amount = Price × VAT Rate

For example, if a product costs Ksh 1,000 and VAT is 16%, then:

  • VAT Amount = 1,000 × 0.16 = Ksh 160
  • Total Price = 1,000 + 160 = Ksh 1,160.

Income Tax is calculated based on income brackets. For instance, if a person earns Ksh 50,000 and the tax rate is 10%, the tax payable is:

  • Income Tax = 50,000 × 0.10 = Ksh 5,000.

Percentage Error in measurement is calculated using the formula:

  • Percentage Error = (|True Value - Measured Value| / True Value) × 100%

If the true value is 20 cm and the measured value is 18 cm, then:

  • Percentage Error = (|20 - 18| / 20) × 100% = 10%.
  • VAT is calculated as Price multiplied by VAT Rate.
  • Income tax depends on the income bracket and applicable rate.
  • Percentage error measures accuracy in measurements.
  • Use absolute difference for percentage error calculation.
  • Always express percentage error as a percentage.

A product costs Ksh 2,000 with a VAT rate of 16%. Calculate the total cost including VAT.

  • VAT Amount = 2,000 × 0.16 = Ksh 320.
  • Total Cost = 2,000 + 320 = Ksh 2,320.
Lesson 4: Understanding Percentages in Real Life

Objective: Percentages (applications: profit, loss, discount, commission)

Percentages are essential in daily financial transactions. They help us calculate profit, loss, discount, and commission. Here’s a breakdown of each application:

  • Profit: Profit is the amount earned after selling a product above its cost price. The formula is:

    Profit = Selling Price (SP) - Cost Price (CP)

    To express profit as a percentage:

    Profit Percentage = (Profit / CP) × 100%

  • Loss: Loss occurs when the selling price is less than the cost price. The formula is:

    Loss = Cost Price (CP) - Selling Price (SP)

    Loss Percentage = (Loss / CP) × 100%

  • Discount: Discount is a reduction on the marked price. To find the selling price after discount:

    Selling Price = Marked Price - Discount

    Discount Percentage = (Discount / Marked Price) × 100%

  • Commission: Commission is a fee paid for services, usually a percentage of sales. Commission = (Commission Rate × Sales) / 100.

Understanding these concepts helps in making informed financial decisions.

  • Profit is calculated as Selling Price minus Cost Price.
  • Loss is determined when Selling Price is less than Cost Price.
  • Discount reduces the marked price of an item.
  • Commission is a percentage of total sales.
  • Percentages are vital for financial literacy.

A shop sells a shirt for Ksh 800, having bought it for Ksh 600. Calculate the profit percentage.

  • Profit = 800 - 600 = Ksh 200.
  • Profit Percentage = (200 / 600) × 100% = 33.33%.

Sample Questions

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1
easySHORT ANSWER2 marks

Name the percentage error if an engineer measures a beam to be 2.4 m when the actual length is 2.5 m. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Actual length = 2.5 m; error = |2.5 - 2.4| = 0.1 m (1 mk)
Percentage error = (0.1 / 2.5) × 100 = 4% (1 mk)
2
easySHORT ANSWER2 marks

A stationery shop purchases a box of pens for Ksh 800 and sells it at a profit margin of 25%. Calculate the selling price of the box of pens. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Profit = 25% of 800; Profit = 0.25 × 800 (1 mk)
Selling price = Cost price + Profit = 800 + 200 = Ksh 1,000 (1 mk)
3
easySHORT ANSWER3 marks

A farmer sold a batch of mangoes for Ksh 3,500 after applying a discount of 15% on the original price. Calculate the original price of the mangoes. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Let original price be P; Selling price = P × (1 - 0.15) (1 mk)
Substitute selling price: 3,500 = P × 0.85 (1 mk)
P = 3,500 / 0.85; Original price = Ksh 4,117.65 (1 mk)
4

A farmer sold a cow for Ksh 80,000 after incurring a cost of Ksh 60,000. Calculate the percentage profit made on the sale. (2 marks)

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Frequently asked questions

What does the KCSE Mathematics topic "Percentages (applications: profit, loss, discount, commission)" cover?

Percentages (applications: profit, loss, discount, commission) covers Express a quantity as a percentage of another and calculate percentage increase and decrease; Calculate profit, loss, discount and commission as percentages and apply to buying and selling scenarios; Solve problems involving taxation (VAT, income tax), insurance premiums and percentage error in measurement, and more, all aligned to the official KNEC KCSE Mathematics syllabus.

How many practice questions are available for Percentages (applications: profit, loss, discount, commission)?

HighMarks has 97 Percentages (applications: profit, loss, discount, commission) practice questions for KCSE Mathematics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Mathematics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Percentages (applications: profit, loss, discount, commission) for the KCSE exam?

Start with the revision notes on this page to refresh the core concepts, then work through the practice questions in increasing difficulty. Sign up for HighMarks to get a personalised study plan that adapts to the topics you keep getting wrong, plus mock exams, subject-wide practice, and detailed performance tracking. See pricing.

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