KS3 Maths · Year 8 · Chapter 1: Percentages · Lesson 2

Percentage increases and decreases

Year 8About 70 minutesCalculator allowed47 marks

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Quick questions to start.

A1
Needed today
Write down the multiplier for an increase of $6%$ .
[1 mark]
Answer
A2
Needed today
Write $0.925$ as a percentage.
[1 mark]
Answer
A3
Last lesson
A loan of $£300$ has simple interest of $2%$ each month. Work out the interest for $5$ months.
[1 mark]
Answer
A4
Year 7
Write $\frac{3}{8}$ as a decimal.
[1 mark]
Answer

Example, then your turn

Year 8

To increase by $15%$ multiply by $1.15$ ; to decrease by $15%$ multiply by $0.85$ . Your teacher works through each example with you. Then try the one beside it.

Example 1

A bike costs $£360$ . The price goes up by $15%$ . Work out the new price.

Hint

100% + 15% = 115%

, so the multiplier is

1.15

B1
The rent on a flat is $£860$ a month. It goes up by $4%$ . Work out the new rent.
[2 marks]
Answer

Example 2

A television costs $£1250$ . In a sale the price is reduced by $17.5%$ . Work out the sale price.

Hint

100% - 17.5% = 82.5%

, so the multiplier is

0.825

B2
A gas bill is $£218.40$ . It goes down by $12.5%$ . Work out the new bill.
[2 marks]
Answer

Example 3

The price of a car falls from $£13 480$ to $£12 750$ . Work out the percentage decrease, to $1$ decimal place.

Hint original

\times

multiplier

=

new, so the multiplier is new

\div

original.

B3
A dog's mass goes up from $64.5$ kg to $71.2$ kg. Work out the percentage increase, to $1$ decimal place.
[2 marks]
Answer

Example 4

The population of a town grew from $38000$ to $107000$ in $60$ years. Work out the percentage increase, to the nearest whole number.

Hint The multiplier is more than

2

, so the increase is more than

100%

B4
The value of a painting rose from $£14 500$ to $£52 200$ . Work out the percentage increase.
[2 marks]
Answer

Example 5

A card is $18$ cm by $12$ cm. A border $1.5$ cm wide is cut off all the way round. Work out the percentage decrease in (i) the perimeter, (ii) the area.

Not drawn accurately

Hint Work out the new length and width first. Each side loses the border at BOTH ends.

B5
A photo is $20$ cm by $12$ cm. A frame $2$ cm wide is put all the way round it. Work out the percentage increase in (i) the perimeter, (ii) the area.
[3 marks]
Not drawn accurately
Answer(i) $\dots\dots %$ (ii) $\dots\dots %$

Practice

Year 8

C1
The multiplier for a price increase is $1.085$ . (i) What is the percentage increase? (ii) What is the multiplier for a decrease of the same percentage?
[2 marks]
Answer(i) $\dots\dots %$ (ii) $\dots\dots$
C2
A rare coin is worth $£450$ . Its value increases by $235%$ . Work out its new value.
[2 marks]
Answer

C3
A dealer buys a watch for $£480$ and sells it for $£612$ . Work out her percentage profit.
[2 marks]
Answer
C4
Ola makes candles. Each one costs her $£6.40$ to make. She wants a profit of at least $35%$ . What is the least price she can sell a candle for?
[2 marks]
Answer
C5
A sign in a shop says, "All prices reduced by $120%$ ." Explain why this cannot be true.
[1 mark]
C6
A rectangle is $25$ cm by $16$ cm. Its length is increased by $20%$ and its width is decreased by $25%$ . Work out the percentage change in its area. Say whether it is an increase or a decrease.
[3 marks]
Not drawn accurately
Answer

Exam-style questions

GCSE Foundation

D1
Beth says, "A change from $640$ to $800$ is an increase of $25%$ . So a change from $800$ to $640$ is a decrease of $25%$ ."
Beth is wrong about the decrease. Explain why, and work out the correct percentage decrease.
[3 marks]
AnswerPercentage decrease $\dots\dots %$

D2
The table shows the price of a house in three years.
(a)
Work out the percentage increase in the price from 2005 to 2012.
[2 marks]
Answer
(b)
Work out the percentage decrease in the price from 2012 to 2020.
[2 marks]
Answer
(c)
Kim says, "From 2005 to 2020 the price went up by $30% - 10% = 20%$ ." Is Kim correct? You must show your working.
[2 marks]
Total for D2: 6 marks
D3
The table shows the sales of three shops last year and this year. Which shop had the greatest percentage increase in sales? You must show your working.
[4 marks]
Answer
D4
A gym membership costs $£36.50$ a month. The price goes up by $8%$ . Ali pays the new price for $12$ months. Work out how much Ali pays altogether.
[3 marks]
Answer

Extension

Stretch

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

E1
A price is increased by $x %$ . Then the new price is decreased by $x %$ . The final price is $4%$ less than the price at the start. Find the value of $x$ .
[4 marks]
Hint 1 · What to try
Try a starting price of $£100$ and a value of $x$ , say $10$ . What is the final price?
Hint 2 · The first line
With $x = 10$ : $100 \times 1.1 \times 0.9 = 99$ , only $1%$ less. You need a bigger $x$ .
Hint 3 · The full method
With $x = 20$ : $100 \times 1.2 \times 0.8 = 96$ , which is $4%$ less. So $x = 20$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can increase or decrease an amount by a percentage with a multiplier.
I can work out a percentage change, including changes over 100%.
I can work out percentage profit and the price for a given profit.
I can explain why a change back is not the same percentage.

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