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GCSE: AQA Unit 1 [calculator allowed]

Ratio and Percentage Examples

Key ratio examples

Example 1

Jack and Jill share some money in the ratio 3:11

If Jill receives 357.50, how much does Jack receive?

We can lay it out in a table

Jack

 

Jill

 

So Jack receives:

Example 2

Dodgy Dan sells old and new cars in the ratio 17:15. What percentage of the cars he sells are new cars?

a)      Add up the parts

b)      So the percentage of new cars is

Key Percentage Examples

Example set 1: Quick percentages on a calculator

 

Increase 230 by 15%

100%+15%=115% so we do:

 

Decrease 432 by 22%

100%-22%=78% so we do:

 

Example set 2: finding percentage changes

The number of people in a school goes up from 620 to 715. What is the percentage increase?

a)      Increase is 715-620=95

b)      So percentage increase is:

 

Generally, we do:

Dodgy Dan hopes to increase his sales by 17%. They go up from 23,000 to 26,500. Has he met his target?

a)      The increase is 26,500-23,000=3500

b)      So percentage increase is:

 

No, he has not met his target!

 

 

 

Example set 3: Exponential growth/compound interest

Peter invests 300 at an interest rate of 7%. How much does he have after 8 years?

Each year sees an increase of 7%.

100% + 7% = 107%, so we need to multiply by 1.07 for each year.

So after eight years he has:

NB: Observe how we have used the power button rather than multiply by 1.07 eight times

 

Example set 4: reverse percentages

Sam buys an antique and a year later it has increased by 13% to 395.50.

How much was it worth originally.

To increase by 13% we know we have to multiply by 1.13.

However, we are looking for the price BEFORE the increase. To find this original price we must reverse this change BY DIVIDING the NEW VALUE by 1.13

 

VAT is added at 20%. A shop-keeper is selling a TV for 4674 (including VAT)

How much VAT has been added?

To increase by 20% we know we have to multiply by 1.20

Therefore, the price BEFORE VAT was added must have been:

 

So, the amount of VAT is 4674 - 3895 = 779