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8.01 Percentage increase and decrease

Worksheet
Percentage increase and decrease
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

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\%.

4

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.

5

A basket of goods was valued at \$43.70 in January 2011. The inflation rate for the year was 8\%. What is the expected cost of the basket of goods in January 2012?

6
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.

7

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\%
8

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.

9

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

10

What does 10\% off the price of a car mean?

11

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?

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.

Repeated percentage change
13

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.

14

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?

15

The price of a phone was increased by 40\% and then again by 40\%.

a

What was the overall percentage increase?

b

Is the overall percentage increase when the price is increased by 40\% twice equal to 2 \times 40\%?

16

The price of a dress was reduced by 30\% and then again by 30\%.

a

What was the overall percentage decrease?

b

Is the overall percentage decrease when the price is reduced by 30\% twice equal to \\ 2 \times 30\%?

17

Find the overall percentage increase of the following:

a

The price of a shirt was increased by 97\% and then again by 97\%.

b

The price of a dress was reduced by 20\% and then increased by 44\%.

c

The price of a dress was increased by 19\% and then reduced by 14\%.

18

The price of a phone was reduced by 25\% and then again by 25\%. Find the overall percentage decrease.

19

After discounting, a clothes dryer sold for \$855. Calculate the original price if the discount was:

a

20\%

b

20\% and 16\% successively

20

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\%

21

A PC originally sells at \$4700.

a

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

b

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

c

Does the order of discounting affect the sale price?

d

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

22

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?

23

Bob has invested heavily in a certain company. One day, it was announced that their factory was damaged by a fire and its share price fell by 40\%. However, when it was announced the next day that the company had insurance and wouldn't be too badly affected, the shares recovered by 40\%.

a

Express the share price after the original announcement as a percentage of the previous day's price.

b

Express the share price after the insurance announcement as a percentage of the price after the original fire announcement.

c

Calculate the final share price as a percentage of the price before either announcement.

d

Hence, evaluate the percentage change over the two years.

e

Is this change an overall increase or decrease?

Goods and services tax
24

Calculate the 10\% GST applicable on the following original prices:

a

\$80

b

\$37

c

\$95

d

\$59

25

Calculate the sales price, including GST, for an item with an original price of \$20.

26

John received a bill of \$68 for consultation and \$10 for herbal supplements from a medical professional. If GST is only applied to the consultation fee, what is the total bill that John must pay?

27

Calculate the GST on an item with a sales price (including GST) of:

a

\$40

b

\$83.90

28

Calculate the original price of the item, before the application of GST for each of the following sales price:

a

\$99

b

\$56.45

c

\$937.70

29

Fruits and vegetables do not incur GST of 10\%. If the total shopping bill is \$109, and fruits and vegetables amount to \$62, what is the cost of the other items prior to adding GST?

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Outcomes

MS11-5

models relevant financial situations using appropriate tools

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