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Find the Original Amount Before a Percentage Change

In this worksheet students will be able to calculate the original value of something after a percentage change has taken place.

'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

Your friend bought you a birthday present in the sale.....cheapskate.....

You want to know how much the item was worth before the sale.

Or they may have missed the sale and had to pay more, because the original price had been increased.

 

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

This key word reverse is going to help us throughout this activity.

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

We know that the radio x 1.40 = £63  just reverse the process (work backwards)  63÷1.40 = £45

 

A packet of washing powder is advertised as having extra '20% extra powder'.

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

Powder x 1.20 = 1.32kg  Let us reverse   1.32 ÷ 1.20 = 1.1kg

 

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 it is a reduction we need to take 8% away from 100% = 92% this is our multiplier.

We now do the  inverse(opposite)

 £586 ÷ 0.92 = £636.96

 

 Let us extend this a little bit

You many get questions that don't appear that straight forward and may need a different approach.

At a hockey game there are 60 children.  This is 20% of everyone at the game.  How many people are at the game?

Think about what you know.   20% = 60    so  20% x 5 = 100% 

60 x 5 = 300 people altogether

One more method you may need to adopt

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% we have to adopt a different approach.  Think about what you know.

If 33% of the shoes are leather the suede shoes make up the remaining 67%.  To make life easy we want to find 1%.

The only numbers we have to work with are for the suede shoes.

4355 ÷ 67 = 65

1% = 65. Therefore 33% = 65 x 33 = 2145

I wonder if they are blue suede shoes?  Ask someone older if you need to.....

 

This latest phone's sale price has increased by 12% to £315 due to high demand. How much did the phone cost before the increase?

Show your answer as £....

Various items of clothing have had various taxes added to them what is the original price of the clothing before tax.

T- shirt  £9.87 tax added 6%

Shorts £7.20 tax added 5%

Jeans £25.40 tax added 20%

Boots £38.25  tax added 16%

Show your answers as £....

Round all answers to 2 decimal places (2 d.p)

Your local electronics store is having a sale.  Calculate the original price of the goods on offer.

Write your answers rounded to 2 decimal places (2.d.p)

Show your answers as £.....

Match up the price increases and  decreases.

All answers have been rounded to the nearest £.

Column A

Column B

Lola's pay increased this week by 5% to £315. Wh...
£474
Zac did up a car and sold it for £750 at a 12% ma...
£300
A washing machine was reduced by 7% in a sale. It ...
£670
A television set was reduced by 12% in a sale to ...
£220
Martha sold her bicycle for £78. This was at a 2...
£1080
I have £545 in the bank at the end of this year f...
£100

At the local fair there were 40 woman which was 25% of all those there.  How many people were at the fair altogether?

 

400

180

160

200

bottles

On a production line  36% of the bottles are glass and the remaining 22400 are plastic.  How many bottles are glass?

380

126

1260

12600

 

house

The population of a village is made up of 28% children and 1152 adults.  How many children are there in the village?

 

448

446

444

442

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 the first year?

Round to the nearest pound throughout your working.

 

 

900

964

950

945

After 6% increase followed by a 9% increase, a doctor earned £2862 per month.  What was the original monthly salary?

Round your answer to the nearest £.

Show your answer as £...

Look at the following bank balances after the percentage interest added.  Select what the original investments were.

Answers have been rounded to 2 decimal places (2 d.p)

 

 £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

This latest phone's sale price has increased by 12% to £315 due to high demand. How much did the phone cost before the increase?

Show your answer as £....

CORRECT ANSWER
£281.25
EDDIE SAYS
If you are unsure it is always useful to write out what you know to help visualise working backwards. Phone x 1.12 = £315 and now let us reverse this £315 ÷ 1.12 = £281.25 This doesn't appear so daunting now does it?
  • Question 2

Various items of clothing have had various taxes added to them what is the original price of the clothing before tax.

T- shirt  £9.87 tax added 6%

Shorts £7.20 tax added 5%

Jeans £25.40 tax added 20%

Boots £38.25  tax added 16%

Show your answers as £....

Round all answers to 2 decimal places (2 d.p)

CORRECT ANSWER
EDDIE SAYS
Here goes £9.87 ÷ 1.06 = £9.31 £7.20 ÷ 1.05 = £6.86 £25.40 ÷ 1.20 = £21.17 £38.25 ÷ 1.16 = £32.98 We had better get shopping before the tax rises..
  • Question 3

Your local electronics store is having a sale.  Calculate the original price of the goods on offer.

Write your answers rounded to 2 decimal places (2.d.p)

Show your answers as £.....

CORRECT ANSWER
EDDIE SAYS
As always with percentages and reductions we need to take the percentage given away from 100 to find the multiplier to work with. As an added bonus there is something else to remember and that is to work backwards. 322 ÷ 0.94 = £342.55 450 ÷ 0.89 = £505.62 190 ÷ 0.92 = £206.52 210 & divide; 0.85 = £247.06 Did you find any bargains? I do love a bargain.
  • Question 4

Match up the price increases and  decreases.

All answers have been rounded to the nearest £.

CORRECT ANSWER

Column A

Column B

Lola's pay increased this week by...
£300
Zac did up a car and sold it for ...
£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
Mixed up answers, don't you just love them? This is a good way to make sure you are comfortable with the methods for finding the original amounts after an increase or the dreaded decrease with two things to remember. Just remember to work backwards. I remember it by thinking 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 £? Even something else to remember.....
  • Question 5

At the local fair there were 40 woman which was 25% of all those there.  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. Remember what you know 25% = 40 25% x 4 = 100% 40 x 4 = 160 I don't like heights so the ferris wheel is out for me.
  • Question 6

bottles

On a production line  36% of the bottles are glass and the remaining 22400 are plastic.  How many bottles are glass?

CORRECT ANSWER
12600
EDDIE SAYS
Oh yes another awkward one. But is good to have all methods covered. It is a case of looking at the question carefully and thinking about what you know. 36% of the bottles are glass so the remaining 64% are plastic. We know that 22400 is 64%. It would make things easier to find 1%. To do this 22400 ÷ 64 =350 350 x 36 = 12600
  • Question 7

 

house

The population of a village is made up of 28% children and 1152 adults.  How many children are there in the village?

 

CORRECT ANSWER
448
EDDIE SAYS
Awkward percentages mean find the 1%. 100% - 28% = 72% 1152 ÷ 72 = 16 28 x 16 = 448 Far easier than walking round 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 the first year?

Round to the nearest pound throughout your working.

 

 

CORRECT ANSWER
964
EDDIE SAYS
This is not as bad as it looks. The salary has increased so we are going to work backwards twice. £21250 ÷ 1.05 =£20,238 rounded to the nearest £ £20,238 ÷ 1.05 = £19, 274 rounded to the nearest £ You are interested in the amount of increase after the first year only. £20,238 - £19,274 =£964
  • Question 9

After 6% increase followed by a 9% increase, a doctor earned £2862 per month.  What was the original monthly salary?

Round your answer to the nearest £.

Show your answer as £...

CORRECT ANSWER
£2500
EDDIE SAYS
A double working backwards thats all. £2862 ÷ 1.08 = £2650 £2650 ÷ 1.06 = £2500 Nice pay rise..
  • Question 10

Look at the following bank balances after the percentage interest added.  Select what the original investments were.

Answers have been rounded to 2 decimal places (2 d.p)

 

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
£1520 ÷ 1.04 = £1461.54 £3520 ÷ 1.03 = £3155.34 Its always useful to be able to work with percentages when investing your hard earned cash. You will be a millionaire soon if you keep investing wisely.
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