KS3 Maths · Year 7 · Chapter 4: Percentages · Lesson 2

Percentage increases and decreases

Year 7About 60 minutesCalculator allowed48 marks

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Date

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Quick questions to start.

A1
Needed today
Write $35%$ as a decimal.
[1 mark]
Answer
A2
Needed today
Work out $15%$ of $£60$ .
[1 mark]
Answer
A3
Last lesson
Write $18$ out of $24$ as a percentage.
[1 mark]
Answer
A4
From chapter 3
A bag holds $3$ red and $5$ blue counters. One is taken at random. Find P(blue).
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

A bike costs $£260$ . Its price goes up by $15%$ . Use a multiplier to work out the new price.

Hint The old price is

100%

. The new price is

100% + 15% = 115%

of it.

B1
A tablet costs $£180$ . Its price goes up by $35%$ . Use a multiplier to work out the new price.
[2 marks]
Answer

Example 2

A coat costs $£85$ . In a sale its price is reduced by $30%$ . Work out the sale price.

Hint After a

30%

cut you pay

100% - 30% = 70%

of the price.

B2
(i) Reduce $£64$ by $15%$ . (ii) Reduce $3.5$ kg by $8%$ .
[3 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$

Example 3

A plant is $24$ cm tall. Its height increases by $175%$ . Work out its new height.

Hint

100% + 175% = 275%

. A multiplier can be more than

2

B3
The population of a town was $18400$ . It increased by $130%$ . Work out the new population.
[2 marks]
Answer

Example 4

VAT of $20%$ is added to a price of $£37.45$ . Work out the price including VAT.

Hint Multiply by

1.2

. Money is written with two decimal places.

B4
A meal costs $£39.99$ . A service charge of $12.5%$ is added. Work out the total cost, to the nearest penny.
[2 marks]
Answer

Practice

Year 7

C1
A shop works out its sale prices by multiplying by $0.65$ . What is the percentage reduction in the sale?
[1 mark]
Answer
C2
Increase $52$ m by $125%$ .
[2 marks]
Answer

C3
A TV costs $£360$ . Shop A takes $25%$ off. Shop B takes $£85$ off. Which shop is cheaper, and by how much?
[3 marks]
Answer
C4
A recipe uses $450$ g of flour. Tom uses $12%$ less flour. How much flour does Tom use?
[2 marks]
Answer
C5
Kai is paid $£8.40$ an hour. His pay goes up by $6%$ . Work out his new hourly pay, to the nearest penny.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
In April $40$ mm of rain fell. In May there was $50%$ less rain than in April. In June there was $50%$ more rain than in May. Sara says, "So June had the same amount of rain as April."
Is Sara correct? You must show your working.
[3 marks]

D2
A shop is planning a sale. The table shows some normal prices.
(a)
Complete the table.
[3 marks]
(b)
Write down the multiplier for a $30%$ reduction.
[1 mark]
Answer
(c)
Max says, "Taking $10%$ off and then another $20%$ off is the same as taking $30%$ off." Use the $£160$ price to show that Max is wrong.
[2 marks]
Total for D2: 6 marks
D3
A car is worth $£14 500$ . In one year its value falls by $18%$ .
(a)
Work out the value of the car after one year.
[2 marks]
Answer
(b)
In the next year its value falls by $18%$ again. Show that the car is then worth less than $£10 000$ .
[2 marks]
Total for D3: 4 marks
D4
A plumber charges $£65$ for each hour of work and $£28$ for parts. VAT of $20%$ is added to the total. A job takes $3$ hours. Work out the total cost of the job, including VAT.
[4 marks]
Answer
D5
In $2000$ a website had $3200$ users. By $2010$ the number of users had increased by $240%$ . By $2020$ the number had fallen by $15%$ from the $2010$ number. How many users did the website have in $2020$ ?
[4 marks]
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A shop increases the price of a jumper by $20%$ . Later it wants to put the price back to what it was before. By what percentage must it reduce the new price? Give your answer to $1$ decimal place.
[4 marks]
Hint 1 · What to try
Choose a price to try, for example $£100$ . What is the new price? How much must come off it?
Hint 2 · The first line
From $£100$ the new price is $£120$ . You must take $£20$ off $£120$ . Write $20$ as a percentage of $120$ .
Hint 3 · The full method
$\frac{20}{120} = \frac{1}{6} = 16.66 \dots %$ , so $16.7%$ . It is not $20%$ , because the $20%$ is now taken from a bigger price.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write the multiplier for a percentage increase or decrease.
I can use a multiplier to increase or decrease an amount.
I can increase an amount by more than 100%.
I can explain why two changes in a row do not just add up.

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