UK Secondary (7-11)
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Unitary Method with Percentages

So far we're feeling pretty confident about finding a certain percentage of an amount, but is there a way to find the total amount after being given a percentage of it? For instance, let's say $40%$40% of a dog's weight is $10$10kg, how heavy is the dog? We can use what is called the unitary method here, which means finding out what one unit of something is first. In our case we're going to find what one percent is first. Let's see how this works in the following diagram:


Can you see how there are three stages in this method? 

1. Start with the amount that we know and its related percentage

2. Convert both numbers (percentage and amount) to what $1%$1% would be

3. Multiply by $100$100 to get $100%$100%, which is the whole


Adding On

Sometimes questions will involve starting amounts over $100%$100%.

For example, say we knew that a bank account was worth $\$770$$770 after $10%$10% interest was paid. 

To find the original $100%$100% we would first need to figure out what the starting percentage is.

If $\$770$$770 is the amount after interest then it equals $100%+10%=110%$100%+10%=110%.

Then to find the total amount we would follow Step $2$2 above and divide everything by $110$110 to get $1%$1%, and then finally multiply by $100$100 to get the whole amount.

So the original amount in the bank account would be:

$\frac{770}{110}\times100$770110×100 $=$= $7\times100$7×100
  $=$= $\$700$$700

Wow, so the unitary method also works for amounts more than $100%$100%!

Worked Examples

Question 1

$12%$12% of a quantity is $24$24.

  1. What is $1%$1% of the quantity?

  2. Hence find the total quantity.

Question 2

Find the number if $10%$10% of the number is $12$12.

Question 3

$6%$6% of a number is $36$36.

  1. Find $1%$1% of the number.

  2. Hence find $36%$36% of the number.

Question 4

After $10%$10% GST was added, the price of an iPod was $£238$£238. What was its original price before GST?

Round your answer to two decimal places.


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