Browse Percentages & growth

61 questions at your level

DifficultyAllLevel 1Level 2Level 3Level 4Level 5

Percentage change and multipliers

24 questions

LessonNot started
Work out 20%20\% of £6060.
●●●●●Level 11 markStart
A jacket costs £8080. In a sale its price is reduced by 25%25\%. Work out the sale price.
●●●●●Level 12 marksStart
5%5\% of 260260 is

Circle your answer.
  • A 5.25.2
  • B 1313
  • C 5252
  • D 130130
●●●●●Level 11 markStart
In a sale, the price of a jacket is reduced from £6464 to £54.4054.40

Work out the percentage reduction. (2 marks)
●●●●●Level 12 marksStart
(a) Increase 240240 by 15%15\% (2 marks)

(b) Work out 35%35\% of 8080 (1 mark)
●●●●●Level 23 marksStart
Sam buys a bike for £240240 and sells it for £306306

Work out his percentage profit. (2 marks)
●●●●●Level 22 marksStart
There are 720720 people at a concert.

38\dfrac{3}{8} of the people are children. 40%40\% of the children are girls.

Work out the number of girls at the concert. [3]
●●●●●Level 23 marksStart
(a) A jacket costs £8080. In a sale its price is reduced by 35%35\%. Work out the sale price. [2]

(b) Write 12.5%12.5\% as a fraction in its simplest form. [1]
●●●●●Level 23 marksStart
Some members of a gym were asked if they used the swimming pool.

45%45\% of the members said yes.

60%60\% of the members who said yes used the pool more than once a week.

What percentage of the members asked used the pool more than once a week?

(2 marks)
●●●●●Level 22 marksStart
The price of a computer game is £24. A shop increases the price by 25%. The game does not sell, so the shop then reduces the new price by 25%.

(a) Work out the final price of the game.

(b) Work out the overall percentage change from the original £24.
●●●●●Level 35 marksStart
A company's annual profit rose from £1.8 million to £2.07 million. Work out the percentage increase in profit.
●●●●●Level 33 marksStart
The number of members of a running club rose from 8080 to 9292.

Work out the percentage increase.
●●●●●Level 32 marksStart
The average attendance at a cinema fell from 250250 to 210210 people per night.

Work out the percentage decrease.
●●●●●Level 32 marksStart
Priya wants to know how much hot chocolate powder she will need for 540540 people at a winter fair.

Each person who has hot chocolate will have 33 mugs of hot chocolate.

17.417.4 g of hot chocolate powder is needed for each mug of hot chocolate.

Priya assumes 45%45\% of the people will have hot chocolate.
(a) Using this assumption, work out the amount of hot chocolate powder Priya needs.

Give your answer correct to the nearest gram.

(4 marks)

Priya's assumption is wrong.

40%40\% of the people will have hot chocolate.
(b) How does this affect your answer to part (a)?

(1 mark)
●●●●●Level 35 marksStart
Callum pays £48 for 360360 eggs.

Callum puts the eggs into boxes. He puts 66 eggs into each box.

Callum sells all the boxes of eggs for £1.10 each box.

Work out Callum's percentage profit.

(3 marks)
●●●●●Level 33 marksStart
A bag of trail mix has a mass of 750750 g.

36%36\% of the mass of the trail mix is raisins and cranberries.

mass of raisins : mass of cranberries =5:4= 5 : 4

Work out the mass of cranberries in the bag.

(3 marks)
●●●●●Level 33 marksStart
Freya, Tomasz and Ines share some beads in the ratio 3:4:113 : 4 : 11

Ines gives 311\frac{3}{11} of her beads to Freya.

Ines then gives 25%25\% of the rest of her beads to Tomasz.

Ines says,

"We each have the same number of beads now."

Is Ines correct?

You must show how you get your answer.

(4 marks)
●●●●●Level 34 marksStart
Kwame, Lena and Priya share some marbles in the ratio 3:4:93 : 4 : 9

Priya gives 13\frac{1}{3} of her marbles to Kwame.

Priya then gives 20%20\% of the rest of her marbles to Lena.

Priya says,

"We each have an equal share of the marbles now."

Is Priya correct?

You must show how you get your answer.

(4 marks)
●●●●●Level 34 marksStart
Two shops sell the same bicycle.
  • Shop A: priced at £320, with 15% off.
  • Shop B: priced at £298, with 10% off.
Work out which shop sells the bicycle more cheaply, and by how much.

You must show your working.
●●●●●Level 44 marksStart
A laptop has a list price of £1850. A retailer applies the following changes in order: a 20% increase for the new model year, then a 5% loyalty discount on that increased price, then 20% VAT is added.

Work out the final price. Give your answer to the nearest penny.
●●●●●Level 44 marksStart
In a maths exam, Aisha scored 63 out of 90 on Paper 1 and 52 out of 80 on Paper 2.

Work out her overall percentage across both papers combined. Give your answer to 1 decimal place.
●●●●●Level 43 marksStart
Leo bought some shares for £12501250.

He later sold them for £10751075.

Work out his percentage loss.
●●●●●Level 42 marksStart
Last year, Zara's monthly rent rose from £650650 to £702702, and her monthly salary rose from £18001800 to £19261926.

Did her rent or her salary rise by the greater percentage? You must show your working.
●●●●●Level 43 marksStart
A town's population is 20 00020\,000.

One year it increases by 10%10\%. The next year it decreases by 10%10\%.

(a) Work out the population after the two changes.

(b) Tom says the population is back where it started. Explain why Tom is wrong.
●●●●●Level 53 marksStart

Reverse percentages

19 questions

LessonNot started
10%10\% of a number is 77. What is the number?
●●●●●Level 11 markStart
25%25\% of a bag of sweets is 88 sweets. How many sweets are in the bag?
●●●●●Level 11 markStart
After a 10%10\% increase, a price is £5555. What was the original price?
●●●●●Level 22 marksStart
In a sale everything is 20%20\% off. A coat's sale price is £4848. What was its price before the sale?
●●●●●Level 22 marksStart
The price of a train ticket increased by 20%20\%.

The new price is £5454

Work out the original price. (3 marks)
●●●●●Level 23 marksStart
(a) The price of a coat including VAT at 20%20\% is £5454. Work out the price before VAT. [2]

(b) A price is increased by 10%10\% three times in a row. Work out the overall percentage increase. [2]
●●●●●Level 24 marksStart
In a sale, all prices are reduced by 25%. A coat costs £57 in the sale. Work out the original price of the coat.
●●●●●Level 33 marksStart
In a sale, all prices are reduced by 20%20\%.

A pair of trainers costs £6868 in the sale.

Work out the original price of the trainers.
●●●●●Level 32 marksStart
In a sale, all normal prices are reduced by 20%20\%.

The sale price of a coat is £6868

Work out the normal price of the coat. (3 marks)
●●●●●Level 33 marksStart
The amount of honey a beekeeper collected this year is 29\dfrac{2}{9} less than the amount she collected last year.

This year the beekeeper collected 15961596 kg of honey.

Work out the amount of honey the beekeeper collected last year.

(3 marks)
●●●●●Level 33 marksStart
After a 5% pay rise, a teacher's salary is £26 250.

(a) Work out the salary before the rise.

(b) The following year the salary rises again, to £27 300. Work out the percentage rise in that second year.
●●●●●Level 44 marksStart
A plumber's bill is £312, which includes VAT charged at 20%. Work out the amount of VAT charged.
●●●●●Level 43 marksStart
A phone is reduced by 30% in a sale to £154. Nadia says the original price was £200.20, because she worked out 30% of £154 and added it on.

(a) Explain the error in Nadia's method.

(b) Work out the correct original price.
●●●●●Level 43 marksStart
The price of a train ticket rose by 8%8\% this year. It now costs £5.945.94.

Work out the price of the ticket before the rise.
●●●●●Level 42 marksStart
A restaurant bill comes to £456456, which includes VAT charged at 20%20\%.

(a) Work out the amount of the bill before VAT was added.

(b) Work out the amount of VAT charged.
●●●●●Level 43 marksStart
After drying, a batch of clay has lost 35%35\% of its weight.

The dried clay weighs 32.532.5 kg.

Work out the weight of the clay before drying.
●●●●●Level 42 marksStart
At the start of 2024 Dev invested some money in a savings account.

The account paid 2.5%2.5\% compound interest each year.

At the end of 2024
  • interest was added to the account
  • then Dev took £500 from the account.
At the end of 2025
  • interest was added to the account
  • then Dev took £1200 from the account.
There was then £5011.50 in the account.

Work out how much money Dev invested at the start of 2024.

You must show all your working.

(4 marks)
●●●●●Level 44 marksStart
A price is increased by 12%, and then that new price is increased by a further 5%. After both increases the price is £176.40. Work out the original price.
●●●●●Level 53 marksStart
The price of a games console was increased by 25%25\%, and the new price was later reduced by 10%10\% in a sale.

The console now costs £405405.

Work out the price before either change.
●●●●●Level 53 marksStart

Compound growth and decay

20 questions

LessonNot started
Write down the multiplier for an increase of 5%5\%.
●●●●●Level 11 markStart
£200200 is put in a savings account paying 3%3\% simple interest per year. How much interest is earned in 44 years?
●●●●●Level 12 marksStart
£500500 is invested at 4%4\% compound interest per year. How much is in the account after 22 years?
●●●●●Level 22 marksStart
Priya invests £40004000 in a savings account.

The account pays compound interest at a rate of 2.4%2.4\% per year.

Work out the value of the investment at the end of 33 years. (3 marks)
●●●●●Level 23 marksStart
(a) The price of a coat including VAT at 20%20\% is £5454. Work out the price before VAT. [2]

(b) A price is increased by 10%10\% three times in a row. Work out the overall percentage increase. [2]
●●●●●Level 24 marksStart
£4000 is invested in an account paying 2.5% compound interest per year. Work out the value of the investment after 3 years. Give your answer to the nearest penny.
●●●●●Level 33 marksStart
£30003000 is invested in an account paying 3%3\% compound interest per year.

Work out the value of the investment after 22 years.
●●●●●Level 32 marksStart
A motorbike is worth £72007200. It depreciates by 12%12\% of its value each year.

Work out the value of the motorbike after 22 years.
●●●●●Level 32 marksStart
A car is bought for £15 00015\,000

Its value depreciates by 12%12\% each year.

Work out the value of the car after 33 years. (3 marks)
●●●●●Level 33 marksStart
£30003000 is invested at 2.5%2.5\% per year compound interest.

After how many complete years will the investment first be worth more than £34003400? You must show your working. [3]
●●●●●Level 33 marksStart
Asha buys a van with a value of £18 000

The value of Asha's van decreases by 12%12\% each year.

Ben buys a van with a value of £15 500

The value of Ben's van decreases by 7%7\% each year.

At the end of 33 years, whose van has the greater value?

You must show how you get your answer.

(4 marks)
●●●●●Level 34 marksStart
A car is worth £18 500. It depreciates by 14% of its value each year. Work out the value of the car after 4 years. Give your answer to the nearest pound.
●●●●●Level 43 marksStart
£6000 is invested for 5 years.
  • Account A pays 4% simple interest per year.
  • Account B pays 3.6% compound interest per year.
Work out which account earns more interest over the 5 years, and by how much. Give your answer to the nearest penny.

You must show your working.
●●●●●Level 44 marksStart
A colony of bacteria has a population of 8000 and grows by 5% each hour.

(a) Write down an expression for the population after tt hours.

(b) Work out the population after 6 hours. Give your answer to the nearest whole number.
●●●●●Level 43 marksStart
£80008000 is invested for 22 years.

The account pays 2%2\% interest in the first year and 3.5%3.5\% interest in the second year.

Work out the value of the investment at the end of the 22 years.
●●●●●Level 43 marksStart
Ola has £20002000 to invest for 44 years.

Account A pays 3%3\% compound interest per year. Account B pays 3.2%3.2\% simple interest per year.

Which account gives more interest over the 44 years, and by how much? (4 marks)
●●●●●Level 44 marksStart
At the start of 2024 Dev invested some money in a savings account.

The account paid 2.5%2.5\% compound interest each year.

At the end of 2024
  • interest was added to the account
  • then Dev took £500 from the account.
At the end of 2025
  • interest was added to the account
  • then Dev took £1200 from the account.
There was then £5011.50 in the account.

Work out how much money Dev invested at the start of 2024.

You must show all your working.

(4 marks)
●●●●●Level 44 marksStart
£2500 is invested at 4.2% compound interest per year. Work out the smallest number of complete years for the value of the investment to first exceed £3000.
●●●●●Level 53 marksStart
£50005000 is invested at r%r\% compound interest per year.

After 22 years the investment is worth £56185618.

Work out the value of rr.
●●●●●Level 53 marksStart
A fishery estimates its fish stock at 40 00040\,000. The stock is falling by 8%8\% each year.

Work out the smallest number of complete years until the stock first falls below 30 00030\,000.
●●●●●Level 53 marksStart