Mathematics Facultypercentages

The Robert Smyth SchoolY10 Topic 5

Mathematics FacultyPercentages

Finding percentage increases / decreases

& percentage profit.

1.(a)Work out 17% of 84 kg.

......

Answer ...... kg

(2)

(b)Write down 1.75% of 840 km.

......

Answer ...... km

(1)

(Total 3 marks)

2.Hassan earns £26 000 per year.
The first £5000 is tax free.
He pays 22% of the remaining salary in tax.

How much tax does he pay?

......

Answer £......

(Total 2 marks)

3.Tom buys 200 tomato plants at a total cost of £40 to sell at a school fair.

He sellsof them at 50p each.

He then reduces the price of the remaining plants by 20%.

(a)Calculate the new price of a tomato plant.

...... …………………………………………………………………………

Answer ...... pence

(3)

(b)At the end of the day there are 18 plants left which have not been sold.

How much money does he receive from selling the tomato plants at the school fair?

...... …………………………………………………………………………

Answer £ ......

(4)

(Total 7 marks)

4.(a)A year ago, Mark was 185 cm tall.

He is now 4.3% taller.

How tall is Mark now?

...... …………………………………………………………………………

Answer ...... cm

(3)

(b)A year ago Vicky weighed 151 lb.

She now weighs 164 lb.

Calculate the percentage increase in Vicky’s weight.

...... …………………………………………………………………………

Answer ...... %

(3)

(Total 6 marks)

5.In 1974 the number of students in a college was 5000.
This year the number of students is 5750.

What is the percentage increase in the number of students in the college?

......

Answer ...... %

(Total 3 marks)

6.Simon weighed 3.7 kg when he was born.
One year later he weighed 10.9 kg.

Calculate the percentage increase in his weight.

......

Answer ...... %

(Total 3 marks)

7.Karl was given £3.20 pocket money each week in 2004.
In 2005, his pocket money was increased to £3.90 each week.

Calculate the percentage increase in Karl’s pocket money.

......

Answer ...... %

(Total 3 marks)

8.Jenny buys a CD for £16.50
Six months later Jenny sells the CD for £13.20

What is the percentage decrease in the value of the CD?

......

Answer ...... %

(Total 3 marks)

9.Mike took 400 books to sell at a Saturday market.
By 3 pm, he had sold 310 books at 80 pence each.

Mike then reduced the selling price of the remaining books to 50 pence each.
He was left with 24 unsold books which he gave away.

(a)Find the total amount Mike received from selling the books.

......

Answer £ ......

(4)

(b)Mike had spent £150 buying the books.
What was Mike’s percentage profit?

......

Answer ...... %

(3)

(Total 7 marks)

10.A shop has a special offer.

SPECIAL OFFER
This Week Only
BUY THREE ITEMS
AND
GET THE CHEAPEST ONE FREE

(a)Ian buys the following items:

A bottle of shampoo priced at£l.75
A bar of soap priced at£1.15
An aftershave spray priced at£2.85

What is Ian’s percentage saving using this special offer?

......

Answer ...... %

(3)

(b)The greatest possible percentage saving is when the three items are all the same price.

Calculate this percentage saving.

......

Answer ...... %

(2)

(Total 5 marks)

Compound interest

1.Barbara put £15 000 in a savings account on January 1st 2001.
Interest of 2% is added to the account on December 31st each year.

(a)How much is in the account on December 31st 2001?

......

Answer £......

(2)

(b)Explain why the amount in the account after three years is £15 000 × 1.023

......

(2)

(Total 4 marks)

2.In January 2002 the population of Africa was 650 000 000.

The population of Africa is increasing at the rate of 2.9% per annum.

(a)Write down the single number that you need to multiply 650 000 000 by to calculate the population of Africa in January 2003.

......

Answer ......

(1)

(b)Assuming Africa’s population continues to increase at the same rate, calculate the population of Africa in January 2020.

......

Answer ......

(3)

(Total 4 marks)

3.In 2000, a motorway was used by 70 000 vehicles each day.
Since 2000, the number of vehicles which used the motorway increased by 6% every year.

How many vehicles used the motorway each day in 2005?
Give your answer to an appropriate degree of accuracy.

......

Answer …………………………………......

(Total 4 marks)

4.Mr Jones buys a new car for £50 000.
The car decreases in value at the rate of 30% each year.
Find the value of the car after two years.

......

Answer £ ………………………………………..

(Total 3 marks)

5.The value of a computer was £800 on 1st January 2003.
Every three months, the value of the computer decreased by 6% of its value at the start of that three months.

What was the value of the computer on 1st January 2004?

......

Answer £ ......

(Total 3 marks)

6.Kim invests £500 for two years, at 4% compound interest, paid yearly.

Amir says that the interest will be £40.

Is Amir correct?

Explain clearly how you obtained your answer.

...... …………………………………………………………………………

(Total 3 marks)

7.Nick invests £10 000 for 3 years at 4% per year compound interest.

How much interest does he earn?

......

Answer £......

(Total 3 marks)

8.James invests £700 for 2 years at 10% per year compound interest.
How much interest does he earn?

......

Answer £ ......

(Total 2 marks)

9.Derek begins an experiment growing bacteria in a laboratory.
He starts with a mass of 200 grams of bacteria at 1 pm on Monday.
Every day the mass of bacteria grows by 15%.

(a)Calculate the mass of bacteria at 1 pm on Tuesday.

......

Answer ...... grams

(2)

(b)Calculate how many days it takes for the mass of bacteria to double.

......

Answer ......

(3)

(Total 5 marks)

10.(a)Clare bought a cello for £1300.
After one year its value increased by 4%.

Find the value of the cello after one year.

......

Answer £ ......

(2)

(b)Ben bought a violin for £1700.
In each year the value of the violin increases by 12% of its value at the start of that year.

Calculate after how many complete years the value of the violin will be at least £2600.

You must show all your working.

......

Answer ...... years

(4)

(Total 6 marks)

11.A special savings account earns 10% per year compound interest.

(a)Jill invests £2500 in the special account.
How much will she have in her account after 2 years?

...... ……………………………………………………………………………..

Answer £ ......

(3)

(b)James also invests in the special account.
After earning interest for one year, he has £1320 in his account.
How much money did James invest?

...... ……………………………………………………………………………..

Answer £ ......

(3) (Total 6 marks)

12.£4500 is invested at 3.2% compound interest per annum.
How many years will it take for the investment to exceed £5000?

…......

Answer ...... years(Total 3 marks)

13.A shopkeeper normally sells his goods at 70% above cost price.

In a sale he reduces his prices by 40%.

What percentage profit does the shopkeeper make on goods sold in the sale?

...... …………………………………………………………………………

Answer ...... %

(Total 3 marks)

Reverse percentages

1.(a)During 2003 the average wage earned by some factory workers in Barnsley rose from £350 to £372.
What was the percentage increase?

......

Answer ...... %

(3)

(b)During 2003 the number of people out of work in Barnsley fell by 8%.
At the end of the year there were 2576 people out of work in Barnsley.
How many people were out of work at the beginning of the year?

......

Answer …......

(3)

(Total 6 marks)

2.(a)Miss Evans earns £240 per week.
She is awarded a pay rise of 3.5%.

Mr Dale earns £220 per week.
He is awarded a pay rise of 4%.

Whose weekly pay increases by the greater amount of money?
You must show all your working.

......

Answer ......

(4)

(b)In 2003 the State Pension was increased by 2% to £78.03.
What was the State Pension before this increase?

......

Answer £ ......

(3)

(Total 7 marks)

3.(a)Mrs Brown’s bill for servicing her car is £96 plus VAT.
VAT is charged at 17.5%.

What is her total bill?

......

Answer £ ......

(3)

(b)Mr Smith’s bill for servicing his car is £185.65 including VAT.

How much was his bill before VAT was added?

......

Answer £ ......

(3)

(Total 6 marks)

4.Anne buys a printer costing £90.
This cost includes VAT at a rate of 17.5%.

How much is the VAT?

......

Answer £ ......

(Total 3 marks)

5.In Portugal, Brian spends €2.80 on ice cream.
This price includes VAT which is 12% in Portugal.

Find the amount of VAT which Brian paid.

...... ………......

Answer € ......

(Total 3 marks)

6.John has 70 books.
This total is 40% more than the number of books that he had one year ago.

How many books did he have one year ago?

......

Answer ......

(Total 3 marks)

7.A special packet of breakfast cereal contains 20% more than a normal packet. The special packet contains 600 g of cereal. How much cereal does the normal packet contain?

......

Answer ...... g

(Total 3 marks)

8.The number of tissues in a packet is reduced by 20%.
The packet now contains 120 tissues.

How many tissues were there in a packet before the 20% reduction?

......

Answer ......

(Total 3 marks)

9.Sam sees this sign in a shop window.

PRICE
REDUCTION
PHONES 45% OFF
NOW £31.90 /

How much was the phone before the price reduction?

......

Answer £ ………………………………………

(Total 3 marks)

10.Mr and Mrs Smith are buying a washing machine in a sale.

What was the original price of the washing machine?

…......

Answer £ ......

(Total 3 marks)

Percentage Problems

1.In a school one Monday morning, 20% of the pupils are in the hall for an assembly.
The other 560 pupils present that morning are not in the assembly.

Find the total number of pupils present that morning.

......

Answer ......

(Total 3 marks)

2.(a)Rob invested £2500 in a building society account at 2% per year compound interest.

Calculate the total amount in the account after three years.

......

Answer £ ......

(3)

(b)Jane invested some money in a building society account.
Interest of 3% was added to the account after one year.
The total in the account after the interest was added was £221.45

How much money did Jane invest?

......

Answer £ ......

(3)

(Total 6 marks)

3.Cobalt-60 is a radioactive substance that decays with time.
The mass of the cobalt reduces by 12% each year.

How many years will it take for 200 kg of cobalt-60 to decay to a mass of less than 120 kg?

......

Answer ...... years

(Total 3 marks)

4.When a ball is dropped onto the floor, it bounces and then rises.
This is shown in the diagram.

The ball rises to 80% of the height from which it is dropped.
The ball is dropped from a height of 4 metres.

(a)Calculate the height of the rise after the first bounce.

......

Answer ...... metres

(1)

(b)The ball bounces a second time.
It rises to 80% of the height of the first rise.

(i)Calculate the height of the second rise.

......

Answer ...... metres

(1)

(ii)The ball carries on bouncing in this way.
Each time it rises to 80% of the last rise.

For how many bounces does it rise to a height greater than 1.75 metres?
You must show your working.

......

Answer ......

(2)

(c)A different ball is dropped onto the floor.
This ball rises to 70% of the height from which it is dropped.
The height of the rise after the first bounce is 1.82 metres.

Calculate the height from which the ball is dropped.

......

Answer ...... metres

(3)

(Total 7 marks)

5.There are 10 windmills in a line up a hillside.
Each windmill produces 20% more energy than the one below it.
The first windmill, the lowest on the hillside, produces 1.7 megawatts of energy.

(a)How much energy does the second windmill produce?

......

Answer ...... megawatts

(1)

(b)How many of the windmills each produce more than 3 megawatts of energy?

......

Answer ......

(3)

(Total 4 marks)

6.Ranjit started work in 2003.
In 2004 he moved to a different job and his pay decreased by 15%.
At the end of each of the years 2004 and 2005 he was given an increase in pay.
The percentage increase in pay was the same each time.
Ranjit worked out that he was now paid 22.4% more than he was paid in 2003.

Calculate the percentage increase that he received at the end of 2004 and 2005.
You must show your working.

......

Answer ...... %

(Total 4 marks)

7.Liz estimated the cost of the material needed to make herself a dress.

When Liz goes to a shop to buy the material, the cost per metre is 40% more than she had estimated.

Liz is informed by the shopkeeper that she had miscalculated the amount of material and she reallyneeds 20% more material than she had estimated.

How much more than her original estimate does the dress material cost?

Give your answer as a percentage of Liz’s original estimate.

...... …………………………………………………………………………

Answer ...... %

(Total 3 marks)

8.A shopkeeper normally sells a dress at 60% more than his cost price of £80. In a sale the price of the dress is reduced until it is only 10% more than his cost price.

By what percentage of the original selling price has the price of the dress been reduced?

......

Answer ...... %

(Total 3 marks)

9.Karen saw a laptop for sale in 2004.
In March 2005, the price of this laptop was reduced by 20%.
In June 2005, the price of this laptop was reduced by one sixth of the March 2005 price.

Compared with the 2004 price, what percentage discount would Karen obtain by buying this laptop in June 2005?

......

Answer ...... %

(Total 4 marks)

10.A shop reduces the price of its dresses by 30%.
As a result it sells 60% more dresses than last month.

Calculate the percentage increase in its takings.

......

Answer ...... %

(Total 4 marks)

11.Carol sells strawberries.
In 2002 she reduced the weight of strawberries in each packet by 20%.
After receiving complaints, she increased the weight in 2003 back to the amount each packet contained in 2001.

What percentage increase did Carol use? Give your answer as a percentage of the contents in a packet in 2002.

......

Answer ...... %

(Total 3 marks)

12.Louise sold some items on the internet for £94.50
She calculated that she made a profit of 26% on the cost price of the items.
However, when doing her calculation she forgot that she spent £3.50 on postage.

Work out her correct percentage profit.

......

Answer ...... %

(Total 6 marks)

The Robert Smyth School1