GCSE Maths · Higher · Chapter 5: Ratio and proportion · Lesson 3

Repeated and reverse percentages

Grades 5–7About 45 minutesCalculator allowed39 marks

Hints online, answers free with an account:
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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Decrease £300 by $25%$ .
[1 mark]
Answer
A2
Last lesson
A car travels 20 km in 0.5 hours. Find its average speed.
[1 mark]
Answer
A3
From chapter 5
6 pens cost £24. Find the cost of 11 pens.
[1 mark]
Answer
A4
Key Stage 3
Simplify $2 x \times 6 x$ .
[1 mark]
Answer

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

£3200 is invested at 4% compound interest per year. Work out its value after 3 years.

Hint The multiplier for one year is

1.04

. Three years means multiplying by it three times.

B1
A boat is worth £26 000. Its value falls by 9% each year. Work out its value after 4 years.
[3 marks]
Answer

Example 2

After a 15% increase, a train fare is £48.30. Work out the fare before the increase.

Hint The new fare is the old fare times

1.15

. Divide to undo it.

B2
After a 35% reduction, a sofa costs £520. Work out its price before the reduction.
[2 marks]
Answer

Grades 5–6

C1
£1800 is invested at 3% simple interest per year. How much is in the account after 4 years?
[2 marks]
Answer
C2
A price goes up by 15% and then down by 20%. Write down one multiplier for the whole change.
[2 marks]
Answer

C3
A town of 5000 people grows by 7% each year. After how many whole years is it first over 7000?
[2 marks]
Answer
C4
A price including VAT at 20% is £75.60. Work out the price before VAT.
[2 marks]
Answer
C5
A house is worth £240 000. Its value rises by 5% in the first year and by 3% in the second year, then falls by 2% in the third year. Work out its value after the 3 years.
[2 marks]
Answer
C6
A bank pays interest of 6% a year, added as 3% every six months. £5000 is invested. Work out its value after 2 years, to the nearest penny.
[2 marks]
Answer
C7
£6250 is invested at compound interest. After 2 years it is worth £7290. Work out the annual rate of interest.
[2 marks]
Answer

Grades 6–7

D1
Zoe says, "If a price falls by 10% each year for 3 years, it falls by 30% altogether."
Explain why Zoe is wrong, and give the actual percentage fall.
[2 marks]

D2
A painting was bought in 2021. Its value goes up by 6% each year. In 2024, three years later, it is worth £8932.62.
(a)
Work out the price paid for the painting in 2021.
[3 marks]
Answer
(b)
Work out its value in 2028. Give your answer to the nearest penny.
[2 marks]
Answer
(c)
In which year is the painting first worth more than twice the price paid for it?
[2 marks]
Answer
Total for D2: 7 marks
D3
Ana invests £6000 at 3.5% simple interest per year. Ben invests £6000 at 3% compound interest per year. After 5 years, who has more money, and by how much? Give your answer to the nearest penny.
[4 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use a multiplier for simple, compound and repeated percentage change.
I can find the original amount from the amount after a percentage change.

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