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Find the Original Amount Before a Percentage Change

In this worksheet, students will apply reverse percentages to find starting amounts before a percentage increase or decrease has occurred.

'Find the Original Amount Before a Percentage Change' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Discrete Growth and Decay

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Sale

 

Imagine that our friend bought us a birthday present in the sale, and we want to know how much the item was worth before the sale.

 

Or we may have missed out on a promotional offer on Black Friday, and want to know how much the price of an item has increased by. 

 

Finding the original amount, before a percentage change took place, is also known as reverse percentages.

The key word here is reverse - remembering this is going to help us throughout this activity.

 

Let's look at reverse percentages in action now in some examples. 

 

 

 

Bright blue radio with handle

 

e.g. A radio sells for £63, after a 40% increase in the cost price.

What was the original cost price? 

 

We know that the radio sells for £63 after a 40% increase, so we can write this as:

c × 1.4 = 63 (where 'c' represents the original cost)

 

If we solve this using normal algebraic rules, we find that:

c = 63 ÷ 1.40 = £45

 

 

 

e.g. A packet of washing powder is advertised as having an extra 20% powder.

If it contains 1.32 kg, what amount would be in the original pack?

 

p × 1.20 = 1.32 kg

p = 1.32 ÷ 1.20 = 1.1 kg

 

 

 

e.g. A television has been reduced by 8% in a sale.

It now costs £586.

What was the cost of the television before the reduction in price?

 

This time, as we need to find a reduction rather than an increase, we need to take 8% away from 100% to find our multiplier:

100 - 8 = 92% or × 0.92

 

 

Now we need to apply the inverse (opposite) operation to an increase, like this:

 £586 ÷ 0.92 = £636.96

 

 

 

Let us extend this a little more now...

 

You could see questions that don't appear as straightforward as these examples, and may require a different approach.

 

Here's an example to illustrate what we mean. 

 

Boy playing hockey in a yellow kit

 

e.g. At a hockey game, there are 60 children present.

This is 20% of the total amount of people at the game.

How many people are present at the game in total?

 

Think about what we know here:

20% = 60 children and 20% × 5 = 100% 

 

So if we multiply 20% by 5, we reach the total amount in this case:

60 × 5 = 300 people

 

 

 

Pair of brown, leather shoes

e.g. In a shoe factory, 33% of the shoes are leather and the remaining 4355 are suede.

How many shoes are leather?

 

As we cannot easily turn 33% into 100% (as we did in the previous example), we have to adopt a different approach here.

 

Think about what we know again.

If 33% of the shoes are leather, the suede shoes must make up the remaining 67%, so:

4355 = 67%

 

To make life easier, we want to find 1%:

4355 ÷ 67 = 65

 

If 1% = 65, then...

33% = 65 × 33 = 2145 shoes

 

 

 

In this activity, we will apply reverse percentages to find starting amounts before a percentage increase or decrease has occurred, using the methods shown above. 

Android mobile phone

 

This phone's sale price has increased by 12% to £315 due to high demand.

 

How much did the phone cost before this increase?

Rack of clothes in a clothing store

 

Various items of clothing have had a different amount of tax added to them.

 

T-shirts cost £9.87 with tax added at 6%.

Shorts cost £7.20 with tax added at 5%.

Jeans cost £25.40 with tax added at 20%.

Shoes cost £38.25 with tax added at 16%.

 

What is the original price of each piece of clothing, before the tax was added? 

 

Round all your answers to 2 decimal places.

Laptop computer with white screen

 

Your local electronics store is having a sale.

 

Calculate the original price of the goods on offer below.

 

Write your answers rounded to 2 decimal places.

Match up the increases or decreases on the left with the correct original amount on the right. 

 

Note, all answers have been rounded to the nearest £.

Column A

Column B

Lola's pay increased this week by 5% to £315. Wha...
£220
Zac restored a car and sold it for £750 at a 12% ...
£474
A washing machine was reduced by 7% in a sale. It ...
£1080
A television set was reduced by 12% in a sale to ...
£670
Martha sold her bicycle for £78. This was at a 22...
£100
I have £545 in the bank at the end of this year f...
£300

Photo of a funfair at night

 

At the local fair, there were 40 women present, which was 25% of the total number of people in attendance.

 

How many people were at the fair altogether?

400

180

160

200

Collection of coloured glass bottles

 

On a production line, 36% of the bottles are glass and the remaining 22,400 are plastic.

 

How many bottles are glass?

380 bottles

126 bottles

1260 bottles

12600 bottles

Cottages on a hill

 

The population of a village is made up of 28% children and 1,152 adults.

 

How many children are there in the village?

448 children

446 children

444 children

442 children

A woman's salary increased by 5% in one year, and then increased the following year by 5% again.  

Her new salary is £21,250.

 

How much was the increase in pounds after her first year in her job?

 

Note, all answer options have been rounded to the nearest £.

£900

£964

£950

£945

Female doctor

 

After a 6% increase followed by a 8% increase, a doctor earned £2862 per month.

 

What was her original monthly salary?

 

Round your answer to the nearest £.

£900

£964

£950

£945

Look at the following bank balances after a percentage interest has been added.

 

Select what the original investments were in each case. 

 

Note, all answers have been rounded to 2 decimal places.

 

 £1461.54£1451.45£3165.87£3155.34
Investment of 4% over 5 years giving £1520
Investment of at 3% over 6 years giving £3250
  • Question 1

Android mobile phone

 

This phone's sale price has increased by 12% to £315 due to high demand.

 

How much did the phone cost before this increase?

CORRECT ANSWER
EDDIE SAYS
Let's start by summarising what we know and then we can work backwards. Let's use P to represent the original price of the phone. P × 1.12 = £315 P = £315 ÷ 1.12 = £281.25
  • Question 2

Rack of clothes in a clothing store

 

Various items of clothing have had a different amount of tax added to them.

 

T-shirts cost £9.87 with tax added at 6%.

Shorts cost £7.20 with tax added at 5%.

Jeans cost £25.40 with tax added at 20%.

Shoes cost £38.25 with tax added at 16%.

 

What is the original price of each piece of clothing, before the tax was added? 

 

Round all your answers to 2 decimal places.

CORRECT ANSWER
EDDIE SAYS
Let's apply the same process here. £9.87 ÷ 1.06 = £9.31 £7.20 ÷ 1.05 = £6.86 £25.40 ÷ 1.20 = £21.17 £38.25 ÷ 1.16 = £32.97 We had better get shopping before the tax rises again!
  • Question 3

Laptop computer with white screen

 

Your local electronics store is having a sale.

 

Calculate the original price of the goods on offer below.

 

Write your answers rounded to 2 decimal places.

CORRECT ANSWER
EDDIE SAYS
As always when working with reductions, we need to take the percentage given away from 100 to find the multiplier to work with. 100 - 6 = 94 or × 0.94 322 ÷ 0.94 = £342.55 100 - 11 = 89% or × 0.89 450 ÷ 0.89 = £505.62 100 - 8 = 92% or × 0.92 190 ÷ 0.92 = £206.52 100 - 15 = 85% or × 0.85 210 ÷ 0.85 = £247.06 Did you find any bargains there? Everyone LOVES a bargain!
  • Question 4

Match up the increases or decreases on the left with the correct original amount on the right. 

 

Note, all answers have been rounded to the nearest £.

CORRECT ANSWER

Column A

Column B

Lola's pay increased this week by...
£300
Zac restored a car and sold it fo...
£670
A washing machine was reduced by ...
£220
A television set was reduced by 1...
£1080
Martha sold her bicycle for £78....
£100
I have £545 in the bank at the e...
£474
EDDIE SAYS
This is a good activity to make sure you are comfortable with the methods for finding the original amounts after an increase or decrease. Just remember to always work backwards. It may help to think "I have to go back to the original." 315 ÷ 1.05 = £300 750 ÷ 1.12 = £670 205 ÷ 0.93 = £220 950 ÷ 0.88 = £1080 78 ÷ 0.78 = £100 545 ÷ 1.15 = £474 Did you remember to round to the nearest £?
  • Question 5

Photo of a funfair at night

 

At the local fair, there were 40 women present, which was 25% of the total number of people in attendance.

 

How many people were at the fair altogether?

CORRECT ANSWER
160
EDDIE SAYS
Just when you think you have cracked it, there is always that awkward question! What do we know in this case? 25% = 40 25% × 4 = 100% We can apply these facts to reason that: 40 × 4 = 160 people
  • Question 6

Collection of coloured glass bottles

 

On a production line, 36% of the bottles are glass and the remaining 22,400 are plastic.

 

How many bottles are glass?

CORRECT ANSWER
12600 bottles
EDDIE SAYS
Oh yes, another awkward one! It is a case of looking at the question carefully and thinking about what we know. 36% of the bottles are glass, which means that the remaining 64% are plastic. We also know that 22400 bottles represent 64% of the total. Let's use this information to find the value of 1%: 22400 ÷ 64 = 350 350 × 36 = 12600 bottles
  • Question 7

Cottages on a hill

 

The population of a village is made up of 28% children and 1,152 adults.

 

How many children are there in the village?

CORRECT ANSWER
448 children
EDDIE SAYS
If a question looks challenging, finding the value of 1% is always the best idea. 100% - 28% = 72% 1152 ÷ 72 = 16 people represent 1% 28% = 28 × 16 = 448 children That was far easier than walking around the village counting children!
  • Question 8

A woman's salary increased by 5% in one year, and then increased the following year by 5% again.  

Her new salary is £21,250.

 

How much was the increase in pounds after her first year in her job?

 

Note, all answer options have been rounded to the nearest £.

CORRECT ANSWER
£964
EDDIE SAYS
This question is not as challenging as it looks! Her salary has increased twice, so we simply need to apply our reverse percentages process two times in a row. £21250 ÷ 1.05 = £20,238 (to the nearest £) £20238 ÷ 1.05 = £19,274 (to the nearest £) We need to find out the total increase over the first year: £20238 - £19274 = £964 Not a bad increase for just one year, right?
  • Question 9

Female doctor

 

After a 6% increase followed by a 8% increase, a doctor earned £2862 per month.

 

What was her original monthly salary?

 

Round your answer to the nearest £.

CORRECT ANSWER
EDDIE SAYS
This question needs the same process as the last - a double decrease, that's all. £2862 ÷ 1.08 = £2650 £2650 ÷ 1.06 = £2500 We can check we have the correct answer by working through the sum in the opposite direction i.e. £2500 × 1.06 × 1.08. Do we reach £2862?
  • Question 10

Look at the following bank balances after a percentage interest has been added.

 

Select what the original investments were in each case. 

 

Note, all answers have been rounded to 2 decimal places.

 

CORRECT ANSWER
 £1461.54£1451.45£3165.87£3155.34
Investment of 4% over 5 years giving £1520
Investment of at 3% over 6 years giving £3250
EDDIE SAYS
We need to work backwards to find the original amount before a percentage increase has been applied. £1520 ÷ 1.04 = £1461.54 £3520 ÷ 1.03 = £3155.34 You can now apply reverse percentages to find starting amounts before a percentage increase or decrease has occurred - you will be a millionaire soon if you keep investing wisely!
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