Write an expression for the value of a commodity after 20 years if its value
decreases at a monthly rate of 2%.
Answers
Answer:
Unit 4 Section 5 : Percentage Increases and Decreases
Often prices are increased or decreased by a percentage.
In this section we consider how to increase or decrease quantities by using percentages.
Example 1
Katie earns £40 per week for her part-time job. She is to be given a 5% pay rise.
How much will she earn per week after the pay rise?
Example 2
The prices of all the televisions in a shop are to be increased by 8%.
Calculate the new price of a television that originally cost £150.
Example 3
In a sale the cost of a computer is reduced by 30%. The normal price of the computer was £900.
Calculate the sale price of the computer.
Exercises
Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.
Question 1
(a) Increase £100 by 20%.
(b) Increase £400 by 30%.
(c) Increase £80 by 25%.
(d) Increase £50 by 6%.
(e) Increase 40 kg by 3%.
(f) Increase 250 m by 7%.
Question 2
(a) Decrease £60 by 30%.
(b) Decrease 8 m by 5%.
(c) Decrease 80 kg by 10%.
(d) Decrease £44 by 20%.
(e) Decrease 90 m by 2%.
(f) Decrease 420 kg by 25%.
Question 3
A company increases the cost of all its products by 5%. Calculate the new price of each of the items listed below:
(a) a tent that previously cost £60
(b) a rucksack that previously cost £15
(c) a sleeping bag that previously cost £24
Question 4
Joe was paid £30 per week for delivering papers. He was given a 3% pay rise.
How much will he now earn each week?
Question 5
A small firm employs 4 staff. They are all given a 4% pay rise. Calculate the new salary for each member of staff.
The original salaries are as follows:
John Smith £24 000
Alice Holland £22 500
Graham Hall £14 000
Emma Graham £8500
Question 6
Rachel puts £50 into a bank account. After one year 5% interest is added to her money. How much does she have then?
Question 7
Add
17 1
2
% VAT to each of the following prices:
(a) £200
(b) £70
(c) £42
Question 8
A rope is 8 m long but it shrinks when it gets wet. What would be the new length of the rope if its length is reduced by:
(a) 2%
m
(b) 7%
m
(c) 12%
m
Question 9
In a sale the prices of each of the items listed below is to be reduced by 35%.
Calculate the sale price of each item.
Coat £28
Jeans £42
Trainers £36
Shirt £14
Question 10
A mountain bike was priced at £180. Its price was increased by 8%. Later, this increased price was reduced by 20% in a sale.
Calculate the sale price of the bike.
Question 11
This is how Caryl works out 15% of 120 in her head.
10% of 120 is 12,
5% of 120 is 6,
so 15% of 120 is 18.
(a)
Copy and complete the following calculations to show
how Caryl can work out
17 1
2
% of 240 in her head.
% of 240 is
% of 240 is
% of 240 is
so
17 1
2
% of 240 is
(b)
Work out 35% of 250.
Question 12
Look at this table:
Birth rate per 1000 population
1961 1994
England 17.6
Wales 17.0 12.2
(a)
In England, from 1961 to 1994, the birth rate fell by 26.1%.
What was the birth rate in England in 1994?
(b)
In Wales, the birth rate also fell.
Calculate the percentage fall from 1961 to 1994.
Note: Give your answer rounded to 1 decimal place.
Question 13
The table shows the land area of each of the World's continents.
Continent Land Area (in 1000 km²)
Africa 30 264
Antarctica 13 209
Asia 44 250
Europe 9 907
North America 24 398
Oceania 8 534
South America 17 793
World 148 355
(a)
Which continent is approximately 12% of the World's land area?
(b)
What percentage of the World's land area is Antarctica?
Note: Give your answer rounded to whole %.
(c)
About 30% of the World's area is land. The rest is water. The amount of land in the World is about 150 million km².
Work out the approximate total area (land and water) of the World.
million km²
Question 14
In 1995, the Alpha Company employed 4000 people. For each of the next 2 years, the number of people employed increased by 10%.
1995 employed 4000 people
1996 employed 10% more people
1997 employed 10% more people
(a)
Tony said:
"Each year, the Alpha Company employed another 400 people."
Was Tony right?
(b)
Which of the calculations below shows how many people worked for the company in 1997:
(i) 4000 × 0.1 × 2
(ii) 4000 × 0.12
(iii) (4000 × 0.1)2
(iv) 4000 × 1.1 × 2
(v) 4000 × 1.12
(vi) (4000 × 1.1)2
(c)
Look at these figures for the Beta Company:
1995 employed n people
1996 employed 20% fewer people
1997 employed 10% more people
Write an expression using n to show how many people the company employed in 1997. Show your working and write your expression as simply as possible.