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10.02 One amount expressed as a percentage of another

Worksheet
One amount expressed as a percentage of another
1

What percentage of the triangles are shaded?

a
b
2

What percentage is 75 out of 100?

3

Write the following fractions as percentages:

a

\dfrac{11}{100}

b

\dfrac{17}{50}

c

\dfrac{3}{5}

d

\dfrac{10}{25}

e

\dfrac{16}{20}

f

\dfrac{33}{150}

g

\dfrac{125}{100}

h

\dfrac{18}{90}

4

Write the following fractions as percentages in mixed number form:

a
\dfrac{2}{3}
b
\dfrac{5}{6}
c
\dfrac{3}{8}
d
\dfrac{5}{3}
5

Write the following quantities as percentages:

a

36 out of 200

b

10 out of 16

c

9 out of 27

d

17 out of 68

6

Find the following percentages, correct to two decimal places:

a

9 as a percentage of 23

b

15 as a percentage of 31

c

12 as a percentage of 32

d

16 as a percentage of 21

7

Write 42 minutes as a percentage of one hour.

8

Write the following as percentages:

a

199 \text{ L} out of 796 \text{ L}

b

15\text{ cm} out of 0.75\text{ m}

c

440\text{ m} out of 35.2\text{ km}

d

25\text{ mm} out of 2\text{ m}

e

60\,000\text{ mm} out of 4.8\text{ km}

f

45 cents out of \$1.80

9

Determine if the statement \dfrac{7}{5}\gt145\% is true or false.

Applications
10

There are 11 boys and 14 girls in a class.

a

Find the total number of students in the class.

b

What percentage of the class are boys?

c

What percentage of the class are girls?

11

A box of fruit contains 8 apples, 8 mandarins, and 4 pineapples.

a

Find the total number of pieces of fruit inside the box.

b

What percentage of the box are apples?

c

What percentage of the box are mandarins?

d

What percentage of the box are pineapples?

e

What percentage of the box are apples and pineapples?

12

A holiday resort in Tasmania reduced its overnight rates from \$242 to \$184.

a

Find the amount that Valentina would save if she is to take advantage of the sale.

b

Hence find the percentage discount, correct to two decimal places.

13

Consider the fact that 1\text{ L} equals 1000\text{ mL}:

a

What percentage of 1\text{ L} is 900\text{ mL} ?

b

Hence, what percentage of 1\text{ L} is 450\text{ mL} ?

14

What percentage is 30 seconds of 3 minutes 30 seconds? Round your answer to two decimal places.

15

275 millilitres of cordial concentrate is diluted in water to make 8 litres of mixed cordial, what percentage of the mixture is concentrate? Round your answer to two decimal places.

16

Roald runs 2100\text{ m} of a 8 \text{ km} race. What percentage of the race does he have left to complete?

17

Lucy is 50 minutes into a 2 hour and 50 minute flight. What percentage of the flight has she completed so far? Round your answer correct to two decimal places.

18

If you sleep for 49 hours in a week, what percentage of the week are you asleep? Round your answer to two decimal places.

19

A painting on a wall covers 1000\,\text{cm}^2, if the wall is 10\,\text{m}^2, what percentage is covered by the painting?

20

A bushfire covers 10\,000\,\text{m}^2 of a national park that is 5 hectares. If 1 hectare is equivalent to 10\,000\,\text{m}^2, what percentage of the park has been impacted by the fire?

21

Sharon is tiling a bathroom floor that is 8\,\text{m}^2, with tiles that are 5 \text{ cm} by 5\text{ cm} . If she has laid 800 tiles, what percentage has she completed?

22

An item with an original price of \$420 is sold with a discount of \$168.

a

Find the discount rate, as a percentage.

b

Find the sales price.

23

A TV normally sells for \$2032.20. If it is on sale, calculate the discount as a percentage of the normal price for the following. Round your answers to two decimal places.

a

The discount is \$303.70.

b

The sales price is \$1765.90.

24

If Michelle earns a \$2916 commission for \$32\,400 in total sales, what is her commission rate?

25

Han bought a plasma TV for \$3450 and later sold it for \$3180.

a

Express the loss as a percentage of the cost price to one decimal place.

b

Express the loss as a percentage of the selling price to one decimal place.

26

James invests \$9000 in the stock market only to see his shares plummet in value to \$3716.

a

How much money, in dollars, did James lose in the stock market?

b

Calculate James' percentage loss, correct to two decimal places.

27

Emma buys a used laptop for \$162 and resells it for \$492 without spending any money on it.

a

How much profit did Emma make on the laptop in dollars?

b

Calculate Emma's percentage profit, correct to two decimal places.

28

A stockbroker bought 544 shares at \$24.75 per share and later sold the shares for a total of \$16\,307. Calculate the percentage profit, correct to two decimal places.

29

For the following:

i

Calculate the absolute amount of the error of the measurement.

ii

Hence, calculate the percentage error, correct to one decimal place.

a

A dishwasher weighs exactly 30.3\text{ kg}, but was measured by Luke to be 35\text{ kg}.

b

The length of a particular desk is exactly 1.33\text{ m}, but was measured by Tara to be 1.4\text{ m}.

c

The exact length of the lunch break taken by an employee was 52.2 minutes, but was measured by the employee themselves to be 45 minutes.

30

The total number of civilian casualties in a particular war was exactly 83\,891, but was assessed by Italy to be 68\,000 and by England to be 100\,000.

a

Calculte the absolute error of Italy's assessment.

b

Calculate the absolute error of England's assessment.

c

Calculate the percentage error of Italy's assessment, correct to one decimal place.

d

Calculate the percentage error of England's assessment, correct to one decimal place.

e

Hence state which country’s assessment was more accurate.

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