KS3 Maths · Year 8 · Chapter 1: Percentages · Lesson 3

Calculating the original value

Year 8About 70 minutesCalculator allowed52 marks

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Quick questions to start.

A1
Needed today
Write down the multiplier for a decrease of $35%$ .
[1 mark]
Answer
A2
Needed today
Work out $336 \div 1.2$ .
[1 mark]
Answer
A3
Last lesson
A price goes up from $£50$ to $£58$ . Work out the percentage increase.
[1 mark]
Answer
A4
Year 7
Work out $30%$ of $70$ .
[1 mark]
Answer

Example, then your turn

Year 8

original $\times$ multiplier $=$ new, so original $=$ new $\div$ multiplier. Your teacher works through each example with you. Then try the one beside it.

Example 1

The number of members of a club went up by $25%$ . There are now $395$ members. How many members were there before the increase?

Hint The

395

125%

of the old number, so the multiplier is

1.25

B1
After a $35%$ increase, a bus fare is $£2.97$ . Work out the fare before the increase.
[2 marks]
Answer

Example 2

In a sale, the price of a coat is reduced by $15%$ . The sale price is $£71.40$ . Work out the price before the sale.

Hint The sale price is

100% - 15% = 85%

of the old price, so the multiplier is

0.85

B2
After a $22%$ decrease, the number of fish in a pond is $312$ . How many fish were there before the decrease?
[2 marks]
Answer

Example 3

A plumber's bill is $£357.60$ . This includes VAT at $20%$ . Work out the bill without VAT.

Hint VAT is added on to the price, so the bill is

120%

of the price without VAT.

B3
A phone costs $£214.80$ , including VAT at $20%$ . Work out the price of the phone without VAT.
[2 marks]
Answer

Example 4

VAT on a gas bill is $5%$ . A gas bill is $£176.40$ , including VAT. How much of the bill is VAT?

Hint Find the bill without VAT first. The VAT is the difference.

B4
A laptop costs $£622.80$ , including VAT at $20%$ . How much of the price is VAT?
[2 marks]
Answer

Example 5

After a $30%$ price rise a toy costs $£78$ . Sam says, " $30%$ of $78$ is $23.40$ , so the old price was $78 - 23.40 = £54.60$ ." Show that Sam is wrong.

Hint The

30%

is a percentage of the OLD price, not of

£78

. Test Sam's answer.

B5
After a $10%$ fall in value, a car is worth $£7200$ . Jo says, "The value before was $7200 \times 1.1 = £7920$ ." Explain why Jo is wrong, and work out the value before the fall.
[3 marks]
AnswerValue before $£ \dots\dots$

Practice

Year 8

C1
After an increase of $2.5%$ , the rent on a shop is $£922.50$ a month. Work out the rent before the increase.
[2 marks]
Answer
C2
A school has $840$ students. This is $5%$ more than last year. (i) How many students did it have last year? (ii) The number goes up by $5%$ again next year. How many students will there be?
[2 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$

C3
Concert tickets are reduced by $30%$ . Each ticket now costs $£24.50$ . Mia buys $4$ tickets. How much does she save because of the reduction?
[3 marks]
Answer
C4
In another country a bike costs $440$ euros without VAT and $541.20$ euros with VAT. Work out the rate of VAT in that country.
[2 marks]
Answer
C5
After a $140%$ increase, the population of a town is $52800$ . Work out the population before the increase.
[2 marks]
Answer
C6
A packet of rice says " $20%$ extra free". The packet now holds $576 g$ . How much rice is in a normal packet?
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Ravi says, "In a $10%$ off sale a jacket costs $£63$ . So the price before the sale was $63 + 6.30 = £69.30$ ."
Ravi is wrong. Explain why, and work out the price before the sale.
[3 marks]
AnswerPrice before the sale $£ \dots\dots$

D2
The table shows three prices. Each price includes VAT at $20%$ .
(a)
Work out the price of the kettle without VAT.
[2 marks]
Answer
(b)
Lena buys all three items. How much VAT does she pay altogether?
[3 marks]
Answer
Total for D2: 5 marks
D3
A theatre increases the price of a ticket by $20%$ to $£18$ . The number of tickets it sells each night falls by $20%$ to $440$ . Does the theatre take more or less money each night than before? By how much? You must show your working.
[4 marks]
Answer $\dots\dots$ by $£ \dots\dots$
D4
Two shops sell the same television. In Shop A the price is $£540$ after a $10%$ discount. In Shop B the price is $£572$ after a $12%$ discount. Which shop had the higher price before its discount? By how much?
[4 marks]
AnswerShop $\dots$ by $£ \dots\dots$
D5
Between 2001 and 2021 the population of a town rose by $18%$ to $70800$ .
(a)
Work out the population in 2001.
[2 marks]
Answer
(b)
Between 1981 and 2001 the population rose by $25%$ . Work out the population in 1981.
[2 marks]
Answer
Total for D5: 4 marks

Extension

Stretch

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

E1
If a price is increased by a certain percentage, it becomes $£84$ . If the same price is decreased by the same percentage, it becomes $£56$ . Find the price and the percentage.
[4 marks]
Hint 1 · What to try
The increase and the decrease are the same amount of money, because they are the same percentage of the same price.
Hint 2 · The first line
The price is halfway between $£56$ and $£84$ .
Hint 3 · The full method
The price is $£70$ . The change is $£14$ , and $14 \div 70 = 0.2$ .
AnswerPrice $£ \dots\dots$ Percentage $\dots\dots %$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can find the original value after a percentage increase or decrease.
I can work out a price without VAT, and how much of a price is VAT.
I can explain why taking the percentage off the new value is wrong.
I can compare original values found from different changes.

Answers and mark scheme

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