﻿ Unit 4 Section 5 : Percentage Increases and Decreases

# 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%. Increase £400 by 30%. Increase £80 by 25%. Increase £50 by 6%. Increase 40 kg by 3%. Increase 250 m by 7%.
Question 2
(a) Decrease £60 by 30%. Decrease 8 m by 5%. Decrease 80 kg by 10%. Decrease £44 by 20%. Decrease 90 m by 2%. 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 a rucksack that previously cost £15 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 £70 £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) (b) 2% m 7% m 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:
 England Wales Birth rate per 1000 population 1961 1994 17.6 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.

Question 13
The table shows the land area of each of the World's continents.
Continent Land Area (in 1000 km²) 30 264 13 209 44 250 9 907 24 398 8 534 17 793 148 355
(a)
Which continent is approximately 12% of the World's land area?

(b)
What percentage of the World's land area is Antarctica?

(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 - (i) (ii) (iii) (iv) (v) (vi) (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