Practice Maths

Profit, Loss and Discount

Key Ideas

Key Terms

cost price
the amount paid to buy or produce an item.
selling price
the amount charged to the customer.
profit / loss
profit = selling price − cost price (when SP > CP); loss = cost price − selling price (when CP > SP). Expressed as a percentage of cost price: % = (amount ÷ cost price) × 100.
discount
a reduction on the original (marked) price; discount % = (discount amount ÷ original price) × 100. Sale price = original × (1 − rate).
GST
Goods and Services Tax; in Australia, 10% is added to the pre-GST price. Price including GST = pre-GST price × 1.10.

Key formulas

% Profit = (profit ÷ cost price) × 100    |    % Loss = (loss ÷ cost price) × 100
Sale price = original price × (1 − discount rate)    |    Price inc. GST = price × 1.10

Hot Tip Profit and loss percentages are always calculated on the cost price (what you paid), not the selling price.

Worked Example

Question: A trader buys a bike for $320 and sells it for $400. Find the profit and percentage profit.

Step 1 — Find the profit.
Profit = $400 − $320 = $80

Step 2 — Find the percentage profit.
% profit = (80 ÷ 320) × 100 = 25%

Profit and Loss: The Basics

In business, the cost price is what you pay to make or buy something. The selling price is what you charge the customer. The difference tells you whether you made a profit or a loss.

Profit = Selling Price − Cost Price   (when selling price > cost price)
Loss = Cost Price − Selling Price   (when cost price > selling price)

Example: You buy a second-hand bike for $150 and sell it online for $210. Profit = $210 − $150 = $60.

Example: A bakery makes muffins for $2 each and sells them for $1.80 at the end of the day. Loss = $2.00 − $1.80 = $0.20 per muffin.

Percentage Profit and Percentage Loss

A dollar amount of profit or loss doesn't tell the whole story. A $60 profit on a $150 item is very different from a $60 profit on a $6 000 item. Percentage profit and loss show the profit/loss relative to the cost price.

% Profit = (Profit ÷ Cost Price) × 100
% Loss = (Loss ÷ Cost Price) × 100

Example (bike above): % Profit = (60 ÷ 150) × 100 = 40%

Always divide by the cost price, not the selling price. The cost price is the original base we measure from.

Discounts: Marked Price vs Sale Price

The marked price (or recommended retail price) is the original price before a discount. The sale price is what you actually pay after the discount is applied.

Discount amount = Marked Price × discount rate (as decimal)
Sale Price = Marked Price − Discount amount

Or use the multiplier directly: Sale Price = Marked Price × (1 − discount rate)

Example: Headphones are marked at $120. There is a 25% discount. Sale price = $120 × 0.75 = $90. You save $30.

Example: A gaming chair is $350 and is 30% off in a sale. Sale price = $350 × 0.70 = $245.

Finding the Original Price from a Sale Price

If you know the sale price and the discount percentage, you can work backwards to find the original marked price.

Sale price = Marked price × (1 − discount rate), so:
Marked price = Sale price ÷ (1 − discount rate)

Example: A jacket is on sale for $68 after a 20% discount. Original price = $68 ÷ 0.80 = $85.
Check: 20% of $85 = $17. $85 − $17 = $68. ✓

A Business Scenario: Putting It All Together

Imagine you run a small online store selling phone cases. You buy each case for $8 (cost price) and sell them for $20 (selling price). Profit = $12. % Profit = (12 ÷ 8) × 100 = 150%.

Now you run a 30% off sale. Sale price = $20 × 0.70 = $14. Profit at sale price = $14 − $8 = $6. % Profit at sale = (6 ÷ 8) × 100 = 75%. Still profitable, but less so. Understanding this helps you decide whether a sale is worth running.

Key tip: Both percentage profit/loss and percentage change use (amount ÷ original) × 100. In profit/loss, the "original" is always the cost price — what you paid to acquire the item. Don't accidentally use the selling price as the denominator or your percentages will be wrong.

Mastery Practice

  1. Find the profit or loss, and the percentage profit or loss on cost price. Fluency

    1. Cost: $50, Selling: $65
    2. Cost: $120, Selling: $90
    3. Cost: $200, Selling: $260
    4. Cost: $80, Selling: $68
    5. Cost: $150, Selling: $225
    6. Cost: $500, Selling: $430
    7. Cost: $75, Selling: $90
    8. Cost: $1000, Selling: $850

  2. Find the discount amount and the sale price. Fluency

    1. Original: $80, discount: 10%
    2. Original: $250, discount: 20%
    3. Original: $640, discount: 25%
    4. Original: $180, discount: 15%
    5. Original: $95, discount: 30%
    6. Original: $1200, discount: 12%
    7. Original: $56, discount: 50%
    8. Original: $420, discount: 35%

  3. Calculate the GST (10%) and the total price including GST. Fluency

    1. Pre-GST price: $60
    2. Pre-GST price: $145
    3. Pre-GST price: $380
    4. Pre-GST price: $2400
    5. Pre-GST price: $17.50
    6. Total price including GST is $165. What was the pre-GST price?
    7. Total including GST is $550. What was the GST amount?

  4. Solve these mixed profit, loss and discount problems. Understanding

    1. A store buys shoes for $90 and sells them at a 40% mark-up. What is the selling price?
    2. A laptop was bought for $1500. After one year it was sold for $1050. Find the percentage loss.
    3. A dress is marked at $160 with a “30% off” sticker. GST of 10% is then added to the sale price. What is the final price?
    4. A retailer wants to make a 25% profit on an item that costs $84 to buy. What should the selling price be?
    5. An item is sold for $78 at a 35% profit. What was the cost price?

  5. Real-world profit, loss and discount problems. Problem Solving

    1. A market trader buys 50 scarves at $12 each and sells 40 of them for $20 each. The remaining 10 are sold at a 50% discount on the selling price. Find the overall profit or loss.
    2. A second-hand shop buys a camera for $150 and sells it for $195.
      1. What is the percentage profit?
      2. If GST must be included in the selling price, what was the pre-GST selling price, and how much GST was collected?
    3. Jess sees two advertised deals on the same $400 item:
      • Deal A: 20% discount, then 10% GST added.
      • Deal B: 10% GST added, then 20% discount applied.
      Which deal is cheaper, or are they the same price? Show your calculations.
    4. A business loses 8% of its $75 000 annual revenue due to bad debts. It then makes a profit of 12% on its remaining revenue. What is the final profit amount?

  6. For each item, find the selling price given the cost price and percentage profit or loss. Fluency

    1. Cost: $60, 25% profit
    2. Cost: $180, 10% loss
    3. Cost: $250, 40% profit
    4. Cost: $45, 20% loss
    5. Cost: $800, 15% profit
    6. Cost: $1200, 8% loss
    7. Cost: $35, 60% profit
    8. Cost: $720, 12.5% loss

  7. Find the cost price given the selling price and percentage profit or loss. Understanding

    1. Selling price $168, 40% profit. What was the cost price?
    2. Selling price $85, 15% loss. What was the cost price?
    3. Selling price $312, 30% profit. What was the cost price?
    4. Selling price $540, 10% loss. What was the cost price?
    5. Selling price $242, includes 10% GST. What was the pre-GST price and what was the GST collected?

  8. Apply discount and GST in combination. Understanding

    1. A TV has a recommended retail price of $1100. A retailer offers 15% off, then adds 10% GST. Find the final price.
    2. An online store offers a 20% discount on a $250 item, then charges $15 postage. What is the total amount paid?
    3. A car dealer marks up a car by 18% on its trade-in value of $12 500. The buyer is then offered a “loyalty discount” of 5% off the marked-up price. Find the final selling price.
    4. A restaurant bill is $180. A 10% service fee is added, then a 20% discount voucher is applied to the total. What is the final amount paid?

  9. Interpret and solve these business scenarios. Understanding

    1. A retailer buys 100 items at $12 each. They sell 70 at $18 each and the remaining 30 at cost price. Find the total profit and the overall percentage profit on the total cost.
    2. A house is bought for $380 000 and sold four years later for $475 000. Find the percentage profit.
    3. Tickets to a show cost $55 each. A group buys 8 tickets and receives a 12% group discount. The group also gets 10% GST added after the discount. What is the total cost for the group?
    4. A business had total costs of $45 000 and total revenue of $52 000. Express the profit as a percentage of the total costs.

  10. Multi-step profit, loss and discount investigation. Problem Solving

    1. A clothing store buys jackets for $80 each and marks them up by 60%. During a sale, it offers a 25% discount on the marked-up price. Does the store still make a profit? If so, what is the percentage profit on cost price?
    2. A used-car dealer buys 5 cars at the following prices: $8000, $11 000, $9500, $12 500, $7000. He spends $1200 on repairs for each car. He sells the first four cars at 25% profit on total cost (cost + repairs) and the fifth car at 10% loss on total cost. Find the overall profit or loss for all 5 cars combined.
    3. A supermarket sells a product at $4.50 including GST. The pre-GST wholesale price the supermarket paid was $2.50. Calculate the supermarket’s pre-GST selling price and its percentage profit on the wholesale price.
    4. An investor buys 200 shares at $8.50 each. The share price falls 12% in the first year, then rises 20% in the second year. What is the value of the investment at the end of year 2? Has the investor made an overall profit or loss, and by how much?
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