1.5.2 Working with Percentage

1.5.2 Working with percentage

As a percentage:

To find ” $ x $ as a percentage of $ y $”

Divide $ x $ by $ y $
Multiply the result by $ 100 $%.

Worked example:

Work out $ $1.92 $ as a percentage of $ 1.60 $.Divide $ 1.92 $by $ 1.60 $$ \frac{1.92}{1.60} $Multiply $ 1.2 $ by $ 100 $%$ 1.2 \times 100 $ %=$ 120 $ %$ 120$%

Percentage of a number:

To find percentage of a number

Multiply percentage by the number.

Work Example

Worked example:

The earth has a surface area of approximately $ 510100000 km^2 $

Water covers $ 70.8 $% of the earth’s surface.

Work out the area of the earth’s surface covered by water.

Multiply $ 70.8 $% by $ 510100000 km^2 $

$ 70.8 $%$ \times $$ 510100000 km^2 $

As % $ = \frac{1}{100} $, So

$ 70.8 \times \frac{1}{100} \times 510100000km^2 $

$ =361150800 km^2 $

$ 361150800 km^2 $

Work Example

Profit/loss Percentages:

Before moving on to profit/loss percentages, you must first understand cost price and selling price.

The price at which an article is made is known as its cost price.
The selling price of an item is the price at which it is sold.

Profit:

If the selling price (S.P.) of an item is higher than the cost price (C.P.), the difference between the two is referred to as profit.

$ Profit \ = \ selling \ price \ – \ cost \ price $

Profit Percentage:

The profit percentage is the profit gained for a cost price of Rs. $ 100 $.

$ Profit \ percentage \ = \frac{profit}{cost \ price} \times 100 $

Loss:

If the selling price (S.P.) of an item is less than the cost price (C.P.), the difference between the two is referred to as loss.

$ Loss \ = \ cost \ price \ – \ selling \ price $

Loss Percentage:

The loss percentage is the loss for a C.P. of Rs. $ 100 $.

$ Loss \ percentage = \frac{loss}{cost \ price} \times 100 $

Increase by a percentage:

To increase a number by a percentage we use a formula which is

$ (1 \ + \ Percentage \ of \ increase)\times original \ amount $

Decrease by a percentage:

To decrease a number by a percentage we use the following formula

$ (1 \ – \ Percentage \ of \ decrease)\times \ original \ amount $

Worked example:

In $ 2019 $, the membership fee of a cycling club is $ $79.50 $.

This is $ 6 $% more than last year .

Find the increase in the cost of membership

Let’s say the cost of membership fee in $ 2019 $ was ‘$ x $’

Put values in $ (1 \ + \ percentage \ of \ increase)\times Original \ amount $

$ (1+6) $ % $ \times x=79.50 $

Solve for ‘$ x $’

$ x= \frac{79.50}{1+6} $ $ = \frac{79.50}{1+ \frac{6}{100} } $ $ =75 $

Now increase in cost of membership is

$ 79.50-75=4.50 $

Work Example

Reverse percentage:

Reverse percentage means working backward to find an original amount, given a percentage of that amount.To find the original amount of a given percentage

Set the percentage to the amount
Divide the equation to get $ 1 $% on one side

Multiply the equation by $ 100 $ to have $ 100 $%

Keep in mind that $ 100 $% of the given value is the original amount

Worked example:

$ 45 $% of a number is $ 36 $. Calculate the original number.
Set the percentage to the amount
$ 45 $% $ =36 $
Divide the equation by $ 45 $
$ \frac{45}{45}$ % $= \frac{36}{45} $
$ 1 $ % $ = \frac{36}{45} $
Multiply both sides by $ 100 $
$ 100 $ % $ = \frac{36}{45} \times 100 $
$ 100 $ % $ =80 $
So original number is $ 80 $

Work Example

Test your self

There were $ 3.08 \times 10^5 $ passengers that made this journey in $ 2018 $.

This was a $ 12 $% decrease in the number of passengers that made this journey in $ 2017 $.

Find the number of passengers that made this journey in $ 2017 $.

Give your answer in standard form.

[3]

Question: 1

The selling price of a dress fabric is $ $2.97 $ per meter, which is an increase of $ 8 $% on the cost price.

Calculate the cost price per meter.

[3]

Question: 2

The price of a house decreased from $ $82500 $ to $ $77500 $.

Calculate the percentage decrease.

[3]

Question: 3

Here is a list of ingredients to make $ 20 $ biscuits.

Find the mass of price as a percentage of the mass of sugar.

[1]

Question: 4

Question 5:

Rowena buys a jacket for $ $40 $ and sells it for $ $45.40 $.

Calculate the percentage profit.

[3]

Question: 5

Curriculum

1.5.2 Working with Percentage

Worked example:

Percentage of a number:

Worked example:

Profit/loss Percentages:

Profit:

Profit Percentage:

Loss:

Loss Percentage:

Increase by a percentage:

Decrease by a percentage:

Worked example:

Reverse percentage:

Worked example:

Test your self

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