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

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 % 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 % of 240 in her head.
% of 240 is
% of 240 is
% of 240 is
so % 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.
ContinentLand Area (in 1000 km²)
Africa30 264
Antarctica13 209
Asia44 250
Europe9 907
North America24 398
Oceania8 534
South America17 793
World148 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?

The workforce increased to 4400 in 1996, so in 1997 they employed an extra 10% of 4400, i.e. an extra 440, bringing the workforce to 4840.
So Tony was wrong about 1997.
(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.

Number of employees in 1997: × × =

Question 15
A clothes shop had a closing down sale. The sale started on Tuesday and finished on Saturday. For each day of the sale, prices were reduced by 15% of the prices on the day before.
(a)
A shirt had a price of £19.95 on Monday. Kevin bought it on Wednesday. How much did he pay?

(b)
Ghita bought a dress on Tuesday for £41.48. What was its price on Monday?

(c)
A jacket had a price of £49.95 on Monday. What was its price on Friday?

(d)
Another shop is reducing its prices each day by 12% of the prices on the day before. How many days would it take for its original prices to be reduced by more than 50%?

days