Year 8 Percentages: Change, Profit and Interest
Key Stage 3 • Ages 12–13 • Beginner
Instructions: Work through the activities in order, showing your calculations in the spaces provided. Use the worked example to help you choose a decimal multiplier, and include units such as £ or years in your answers.
Increase or Decrease?
For an increase, add the percentage to 100%; for a decrease, subtract it from 100%. Write the resulting multiplier, then calculate the new amount. For example, a 10% increase uses 1.10, so £20 × 1.10 = £22.
1. Increase £40 by 10%. New amount:
2. Decrease £80 by 25%. New amount:
3. Increase 60 kg by 15%. New amount:
4. Decrease £120 by 5%. New amount:
Choose the Decimal Multiplier
Write the decimal multiplier for each percentage change. Then use it to calculate the new amount. An increase multiplier is greater than 1; a decrease multiplier is less than 1.
1. Increase £50 by 20%. Multiplier: New amount:
2. Decrease £200 by 30%. Multiplier: New amount:
3. Increase 80 points by 5%. Multiplier: New amount:
4. Decrease £64 by 12.5%. Multiplier: New amount:
Calculate Percentage Change
Find the difference between the starting and final amounts. Divide the difference by the starting amount, then multiply by 100. State whether the change is an increase or a decrease.
1. A plant grows from 40 cm to 50 cm. Find the percentage change.
2. A jacket’s price falls from £80 to £68. Find the percentage change.
3. A club’s membership rises from 120 to 150 people. Find the percentage change.
4. A phone’s value falls from £240 to £180. Find the percentage change.
Profit and Loss
Compare the selling price with the cost price to find the profit or loss. Calculate the percentage using the cost price as the starting amount: difference ÷ cost price × 100.
1. A shop buys a bag for £20 and sells it for £25. Find the profit and percentage profit.
2. A bicycle costs a seller £150 and is sold for £135. Find the loss and percentage loss.
3. A game is bought for £40 and sold for £50. Find the profit and percentage profit.
4. A table costs £80 and is sold for £68. Find the loss and percentage loss.
Simple Interest
Use simple interest: interest = starting amount × annual interest rate × number of years. Write the rate as a decimal. Add the interest to the starting amount to find the total.
1. Find the simple interest on £200 at 5% per year for 2 years. Then find the total amount.
2. Find the simple interest on £500 at 4% per year for 3 years. Then find the total amount.
3. Find the simple interest on £120 at 10% per year for 2 years. Then find the total amount.
4. Find the simple interest on £800 at 2.5% per year for 4 years. Then find the total amount.
Activity 1: £44 ; £60 ; 69 kg ; £114
Activity 2: 1.20, £60 ; 0.70, £140 ; 1.05, 84 points ; 0.875, £56
Activity 3: 25% increase ; 15% decrease ; 25% increase ; 25% decrease
Activity 4: £5 profit, 25% profit ; £15 loss, 10% loss ; £10 profit, 25% profit ; £12 loss, 15% loss
Activity 5: £20 interest, £220 total ; £60 interest, £560 total ; £24 interest, £144 total ; £80 interest, £880 total
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