CSEC MATHEMATICS · MODULE 1 · LESSON A5

Profit, Loss, Discount and Sales Tax

Cost price, selling price and marked price; profit and loss as amounts and percentages; discount; mark-up; sales tax; and working backwards to the original price.

Fundamentals of Secondary Level MathematicsM1 2.1M1 2.2M1 2.3M1 2.4≈ 35 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON A5 · EXPLAINER

Profit, Loss, Discount and Sales Tax

Every shop, every sale, every bill — consumer arithmetic is the most “real-life” maths in the syllabus, and it is worth marks in every Paper 02.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Profit / loss

Profit = SP − CP. Loss = CP − SP.

% profit / loss

(profit or loss ÷ cost price) × 100. Always the COST price.

Discount

Discount = % × marked price. Sale price = marked price − discount (or × (1 − r/100)).

Mark-up

SP = CP × (1 + mark-up %/100). Mark-up is a % of the cost price.

Sales tax

Price with tax = price × (1 + r/100). Tax = r% × price before tax.

Reverse percentages

Divide by the multiplier: ÷ 0.8 (after 20% off), ÷ 1.15 (including 15% tax).

Amounts then %

Find the dollar profit / loss / discount first, then convert to a percentage.

Sensible answers

A discount lowers the price; a mark-up or tax raises it. Check the direction.

EXAM TIPS & COMMON MISTAKES

  • “Percentage profit” is on COST price unless the question says “percentage of the selling price”.
  • In “show that …” questions (like “show that the cost price is $2.35”) write every step; you are marked on the method, not the answer you were given.
  • Reverse problems: divide by 0.8 or 1.15 — never subtract or add a percentage of the final price.
  • Write money to 2 decimal places, with the $ sign, and state profit or loss in words.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

Adapted from CSEC P1 May/June 2024 (discount item)

1. A dress which costs $180.00 is being sold at a discount of 10%. The amount of the discount is

Answer: D. 10% of 180 = $18.
CSEC Paper 01 style · SO 2.2

2. A shopkeeper buys an item for $80 and sells it for $100. His percentage profit is

Answer: B. Profit $20; 20/80 × 100 = 25%.
CSEC Paper 01 style · SO 2.2

3. An article bought for $250 is sold for $200. The percentage loss is

Answer: B. Loss $50; 50/250 × 100 = 20%.
CSEC Paper 01 style · SO 2.4

4. After a discount of 20%, the price of a bag is $64. The original price was

Answer: A. 64 is 80% of the original: 64 ÷ 0.8 = $80.
CSEC Paper 01 style · SO 2.1

5. A television costs $200 before 15% sales tax is added. The total price is

Answer: B. 200 × 1.15 = $230.
CSEC Paper 01 style · SO 2.4

6. A trader wishes to make a profit of 30% on an article that cost him $400. He must sell it for

Answer: C. 400 × 1.30 = $520.
CSEC Paper 01 style · SO 2.3

7. An item marked at $80 is sold for $68. The percentage discount is

Answer: B. Discount $12; 12/80 × 100 = 15%.
CSEC Paper 01 style · SO 2.4

8. A shop marks up the cost price of a jacket, $150, by 40%. The marked price is

Answer: D. 150 × 1.40 = $210.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (16 marks in total). Show all your working — method marks count. Your answers are saved on this device.

CSEC Paper 02 style · Module 1 (Consumer Arithmetic)

Question 1 [9 marks]

A shopkeeper sold 12 boxes of juice at $3.34 each. His total profit on the boxes was $11.88.

(a) Show that the cost price of one box of juice was $2.35. [3]

MARK SCHEME — (a) (max 3)

(b) Calculate the percentage profit on each box, correct to 1 decimal place. [2]

MARK SCHEME — (b) (max 2)

(c) At a sale he reduces the selling price by 15%. Calculate the new selling price of one box. [2]

MARK SCHEME — (c) (max 2)

(d) Does he still make a profit at the sale price? Justify your answer. [2]

MARK SCHEME — (d) (max 2)

CSEC Paper 02 style · Module 1 (Discount and tax)

Question 2 [7 marks]

A laptop is marked at $2 400. In a sale the shop offers a 15% discount. Sales tax of 12.5% is then added to the sale price.

(a) Calculate the amount of the discount. [1]

MARK SCHEME — (a) (max 1)

(b) Calculate the sale price before tax. [1]

MARK SCHEME — (b) (max 1)

(c) Calculate the total amount a customer pays, including tax. [2]

MARK SCHEME — (c) (max 2)

(d) The shop bought the laptop for $1 800. Calculate its percentage profit on the sale price before tax. [3]

MARK SCHEME — (d) (max 3)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.