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1.02 Percentage increase and decrease

Worksheet
Percentage increase
1
a

Find 30\% of 1500 and add your answer to the original amount of 1500.

b

Calculate 130\% of 1500.

c

Are your answers to (a) and (b) the same? Explain why this is.

2

What percentage should a quantity be multiplied by in order to increase the quantity by:

a
17\%
b
5\%
c
40\%
d
9.4\%
e
33.51\%
f
27.275\%
g
13\dfrac{3}{4}\%
h
112\%
3

What decimal should a quantity be multiplied by in order to increase the quantity by:

a
3\%
b
48\%
c
24.8\%
d
7.7\%
e
99\dfrac{1}{2}\%
f
150\%
4

Increase:

a
700 by 10\%
b
45\text{ cm} by 71\%
c
\$7 by 106\%
d
22.6\text{ kg} by 18\dfrac{3}{4}\%
e
260\text{ L} by 0.8\%
Percentage decrease
5
a

Find 12\% of 1800 and subtract your answer from the original amount of 1800.

b

Calculate 88\% of 1800.

c

Are your answers to (a) and (b) the same? Explain why this is.

6

What percentage should a quantity be multiplied by in order to decrease the quantity by:

a
10\%
b
57\%
c
5\%
d
75\%
e
20.7\%
f
15.7\%
g
85\dfrac{2}{3}\%
h
0.8\%
7

What decimal should a quantity be multiplied by in order to increase the quantity by:

a
9\%
b
43\%
c
6.6\%
d
10.25\%
e
99\dfrac{1}{2}\%
f
27.275\%
8

Decrease:

a
47 by 74\%.
b
7 by 15\%.
c
22.7\text{ m} by 24\%.
d
\$32 by 0.6\%.
e
10.8\text{ g} by 2.6\%.
f
0.25\text{ L} by \dfrac{4}{5}\%.
Applications
9

Very Cheap Auto car company is having a sale such that car prices are discounted by 10\%. If the original price of a car was \$12\,500, find the discounted price of the car.

10

A bag of potatoes weighs 50\text{ kg}. When more potatoes are added, the weight of the bag increases by 35\% find the new weight of the bag of potatoes.

11

A bag of rice weighs 100\text{ kg}. When some rice is poured out, the weight of the bag decreases by 30\%. Find the new weight of the bag of rice.

12

Duncan is going to buy a hat that is marked as 25\% off. The original price was \$30.

a

Find the discount amount.

b

Find the discounted price that Duncan will pay for the hat.

13

Steph is going to buy a dress that is marked as 75\% off. The original price was \$36.

a

What is the value of the discount?

b

What is the price that Steph will pay for the dress?

14

A tennis racket marked at a price of \$90 is advertised to be selling at 45\% off the marked price. Find the discounted price.

15

Christa is going to buy an eraser from a stationery store that is having a storewide 10\% off sale. The original price of the eraser was \$6.

a

What is the value of the discount?

b

What is the price that Christa will pay for the eraser?

16

Andrew is going to buy a jumper that is marked as 30\% off. The original price was \$40.

a

What is the value of the discount?

b

What is the price that Andrew will pay for the jumper?

17

Edward is going to buy a scarf that is marked at 25\% off. The original price is \$26.

a

What is the value of the discount?

b

What is the price that Edward will pay for the scarf?

18

A music store advertises 15\% off all CDs and DVDs. A CD is normally priced at \$16.

a

Find the amount of the discount on this CD.

b

Find the discounted price of the CD.

19

A holiday resort in Tasmania reduced its overnight rates from \$232 to \$120.

a

Find the value of the discount.

b

Find the percentage discount on the original price to two decimal places.

20

A sled sells for \$300 but is now on sale for \$255.

a

By how much has the price of the sled been decreased?

b

Hence, find the percentage discount on the sled.

21

Two book sellers advertised a sale:

  • Honest Anne offered 20\% off the original price of her books.

  • Fair Freddie offered up to 50\% off the original price of his books.

a

Fiona bought books from Honest Anne. The total original price of her books was \$130. Find the value of the discount she received?

b

How much did Fiona pay Honest Anne for the books?

c

At Fair Freddie's, Sarah bought the same books as Fiona at the same original price. She was given 10\% off on the first \$100 worth of books, and 50\% off for the remainder of the original price.

Find the total discount Sarah received on her purchase.

d

What amount did Sarah pay Fair Freddie for the books?

e

Who paid the cheapest price: Fiona or Sarah?

22

Megamart Shoes is having a "choose your own discount" sale. When you buy two pairs of shoes you can choose either of the discount options below.

  • Option 1: 18\% off each pair.

  • Option 2: 40\%off the cheaper pair.

If you are buying two pairs of shoes, one priced at \$68 and the other \$112, which discount option is better?

23

A clothing store works on a markup of 65\%. What would the store charge their customers for the following items:

a

A dress with a cost price of \$22

b

A jumper with a cost price of \$15

c

Pants with a cost price of \$30

d

A coat with a cost price of \$38

24

A laptop is originally priced at \$700. Successive discounts of 12\% and 4\% are applied to the cost of the laptop.

a

Find the final price of the laptop.

b

Find the total discount received.

25

A dining table selling for \$1000 is discounted at 5\% and then again at 6\%.

a

What is the price of the dining table after the first discount is applied?

b

What is the price of the dining table after the second discount is applied?

c

The percentage discount is changed by adding the previous percentages (5\%+6\%) to get 11\%. Find the new discounted price.

d

Is a single discount of 11\% equal to successive discounts of 5\% and 6\%?

e

What is the single discount rate that is equivalent to successive discounts of 5\% and 6\%? Give your answer as a percentage to one decimal place.

26

Which offer gives the greater discount?

a

Offer 1: a single discount of 13\%

Offer 2: successive discounts of 6\% and 11\%

b

Offer 1: a single discount of 16\%

Offer 2: successive discounts of 5\% and 11\%

27

Shares which originally cost \$24 each increase in value by 5\%, then they increase again by 9\%.

a

What is the cost of the shares after the first increase?

b

What is the cost of the shares after the second increase?

c

By how much has the share price increased overall?

d

What overall percentage increase is this equivalent to? Round your answer to two decimal places.

28

A set of professional knives for chefs originally cost \$1900 and is now on sale at 20\% off. A chef receives a further 9\% trade discount.

a

What is the final cost of the set to a chef?

b

How much overall would be saved in comparison to the original price?

c

What overall percentage discount is this equivalent to? Round your answer to two decimal places.

29

A PC originally sells at \$4700.

a

Calculate its sales price after successive discounts of 6\% and 9\%.

b

Calculate its sales price after successive discounts of 9\% and 6\%.

c

Does the order of discounting affect the sales price?

d

Calculate its sales price after successive discounts of 8\%, 7\% and 5\%.

30

The price of a heater selling for \$234 is initially discounted by 14\% and later marked up by 14\%. What is the final sales price?

31

The Run4Fun charity race is increasing in popularity. A year ago 60\,000 people registered to run, and this number is expected to increase by 6\% this year and then by another 8\% next year. How many people are expected to run next year?

32

Quentin wants to buy a jacket that is originally priced at \$220 and is on sale at 14\% off. The jacket is then further discounted by 18\%.

a

What is the final selling price of the jacket?

b

What overall percentage discount is this equivalent to? Round your answer to two decimal places.

c

Quentin believes that if the discounts are applied in the reverse order (that is the 18\% discount first and then the 14\% discount) he will save more money. Is he correct? Explain your answer.

33

A plumber buys bathroom fixtures for a job that cost \$1100 but are on sale at 15\% off. The plumber receives a further 13\% trade discount after the sale discount is taken off.

a

What is the final cost of the set to the plumber?

b

What overall percentage discount is this equivalent to? Round your answer to two decimal places.

c

The plumber was expecting to save \$308, explain what his misunderstanding must have been.

d

Is the overall percentage discount equivalent to discounts applied repeatedly always less than the sum of the individual percentage discounts?

34

The price of a shirt was reduced by 10\% and then increased by 10\%. What was the overall percentage decrease?

35

The price of a dress was reduced by 20\% and then increased by 44\%. What was the overall percentage increase?

36

A country's GDP (Gross Domestic Product) contracted by 4\% one year due to a drought, but then grew by 6\% the next year when the weather returned to normal.

a

Express the country's GDP during the drought as a percentage of the previous year's GDP.

b

Express the country's GDP in the year after the drought as a percentage of the drought affected GDP.

c

Calculate the new GDP as a percentage of the original.

d

Hence, evaluate the percentage change over the two years.

e

Is this change an overall increase or decrease?

37

The price of a laptop is increased by 10\%. Then later this new price is decreased by 10\%. Is the final price of the laptop the same as the original price? Explain your answer.

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Outcomes

1.1.1.6

apply percentage increase or decrease in various contexts, e.g. determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest

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