Year 9 Percentages Worksheet - Intermediate

Year 9 Percentages worksheet for Year 9 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Percentagesintermediate

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Percentages in Action: Year 9 Challenge

Year 9 • Ages 13–14 • Intermediate

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Instructions: Show clear working for each problem and include units where needed. Look for efficient methods: a multiplier can be quicker than finding each percentage separately. Check whether a percentage change is applied once or repeatedly.

Work Backwards: Reverse Percentages

Find the original amount before the percentage change. Identify the percentage of the original that remains or is represented by the final amount, then divide by that percentage. Show your working and include the correct units.

1. After a 20% reduction, a coat costs £72. Find its original price.

2. A bicycle’s price increases by 15% to £345. Find its price before the increase.

3. After a 12% discount, a games console costs £220. Find its original price.

4. A town’s population decreases by 8% to 27,600. Find its population before the decrease.

Compound Interest

Use a multiplier for each year: multiply by 1 plus the interest rate written as a decimal. Apply the multiplier once per year, then round money to the nearest penny. Show the calculation that leads to each answer.

1. £500 is invested at 4% compound interest per year for 2 years. Find the final balance. [3 marks]

2. £1,200 is invested at 3% compound interest per year for 3 years. Find the final balance. [3 marks]

3. £800 is invested at 5% compound interest per year for 2 years. Find the total interest earned. [3 marks]

4. £2,000 is invested at 2.5% compound interest per year for 3 years. Find the final balance. [3 marks]

Repeated Percentage Change

A repeated percentage change means the next change is calculated from the new amount, not the starting amount. Use a multiplier for each change and state whether the final amount is greater or smaller than the start.

1. A £240 item increases in price by 10% each year for 2 years. Find its final price. [3 marks]

2. A £600 machine loses 15% of its value each year for 2 years. Find its value after 2 years. [3 marks]

3. A population of 8,000 grows by 5% each year for 3 years. Find the population after 3 years. [3 marks]

4. A £160 jacket is reduced by 25%, then its reduced price is increased by 25%. Find the final price. [3 marks]

Percentages Greater Than 100%

Remember that 100% represents the whole amount, so a percentage greater than 100% represents more than the whole. Convert the percentage to a multiplier or fraction of the original amount. Include units in your answers.

1. Find 135% of £240.

2. A water tank holds 80 litres. A second tank holds 175% of this amount. How many litres does the second tank hold?

3. A charity raises £1,250, which is 125% of its target. What was the target?

4. A runner completes 140% of a 15 km training distance. How far does the runner travel?

Choose an Efficient Method

For each context problem, choose a suitable efficient method, such as a percentage multiplier, a unitary method, or a simple percentage split. Calculate the answer and show enough working to make your method clear. Round money to the nearest penny where necessary.

1. A shop offers 20% off a £75 coat. Find the sale price using one efficient calculation. [3 marks]

2. A train ticket costs £48, then increases by 12.5%. Find the new price using an efficient method. [3 marks]

3. A café bill of £64 is shared equally by 4 friends. Each friend adds a 10% tip to their share. How much does each friend pay? [3 marks]

4. A laptop costing £640 is reduced by 15%. A customer has a £550 budget. Is the reduced price within the budget, and by how much? [3 marks]

Answer Key

Activity 1: £90 ; £300 ; £250 ; 30,000

Activity 2: £540.80 ; £1,311.27 ; £82 ; £2,153.78

Activity 3: £290.40 ; £433.50 ; 9,261 ; £150

Activity 4: £324 ; 140 litres ; £1,000 ; 21 km

Activity 5: £60 ; £54 ; £17.60 ; Yes, it is within budget by £6