Lesson video

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Hi everyone, in this lesson, we're going to be finding out about reverse percentages.

Hi Rob, if I would say 30% of a number is 54, could you find the original number? Here's 30%.

That is all EQUAL to 54 , by DIVIDING by three, I could find 10%.

10% of the number is 54 DIVIDED by three, which EQUALS 18.

The original number is a 100%.

So am MULTIPLYING 10% by 10 finds me a 100%.

That means the original number is 180%.

6% of a number is 18.

Let's find the original number.

If I know 6% is EQUAL to 18 , then DIVIDING, by six will find me 1% of the original number.

1% in this case is EQUAL to three.

If 1% is equal to three, then MULTIPLYING by a 100 will find me the original number three TIMES by 100, the original number to be 300, 6% of 300 is EQUAL to 18.

27% of the number is 67.


Let's find the number.

If I know that 27% is EQUAL to 67.

5, then it would be helpful for me to be able to find 1%.

That's easy.

Just DIVID both sides by 27.

That means that 1% is EQUAL to 2.


The original number is 100% so MULTIPLYING both sides by a 100 or find me a 100% is EQUAL to 250, 27% of 250 is 67.

5, so here are some examples for you to try pause video and return to check your answers.

Here's the solutions to question number one, you don't have to use bar models, but are a useful tool that really helped me visualise what's happening with certain questions.

Here's my bar model for question one, B Erica was given a pay rise of 5%.

A new wage is nine Pounds and 87 Pounds an hour.

What was the previous wage per hour? This question is asking us to find the original wage.

The original wage is a 100%.

A new wage is a 100% PLUS the pay rise of 5% that is equal to 105%, 105% is equal to nine pounds and 87 B by DIVIDING both sides by 105 means we can calculate what 1% is.

1% is equal to not 0.

09 volt, by MULTIPLYING by a 100, allows us to find her original wage of nine pounds, 40 pounds, per hour.

Victor bought coat for 60 pounds after a 25% sale.

How much was the coat before the sale.

Before the sale is the original price of the coat.

That is a 100%.

The sale is 25% off the original price.

25% off, a 100% will find me , 75%.

The price of the coat was 60 Pounds.

We want to work out a 100%.

75% is EQUAL to 60 pounds to find 1% DIVIDE both sides, by 75, MULTIPLYING both sides by a 100.

We'll find that a 100% is EQUAL to 80 Pounds.

The price of the coat before the sale was 80 Pounds.

Here's some questions for you to try pause the video and return to check your answers.

Here are the solutions to questions two and three.

These types of questions are inverse percentage questions.

One of the tricky things to do with exams is actually recognise what type of percentage question is being asked.

That's something you need to practise by trying a variety of different percentage style questions.