TopIC

6 Percentage
FindingPercentages Practice 6.1

cohe the following word problems. Show your working clearly.

Solve
The original price of a car was $60 000. It was sold at $48 000. What percentage of the origind
1. the selling price?
Drice of the car was

2. osephine spent of her money on a dress and of the remainder on a jacket. What
percentage ot her money did she have left?

3. A piece of land has an area of 4400 m2. A playground occupies 550 m2 of the land and a pond
occupies another 550 m2. What percentage of the land is occupied by the playground and the
pond together?

83
 stuffed toys and 115 are tovrahn S.
There are 500 toys in a ofthe toys are
shop.
4 are not stuffed toys?
percentage of the toys
olb) What
What percentage of the toys are
not stuffed toys toy robots?
or

5. John, Tim and Alice received $20, $48 and S52 respectively from their mother. What percentano
of the total amount given to the three children did Tim receive? age

6. Rachel bought a laptop at a discounted

$2000. What percentage of the original
price of $1600. The original price of the laptop was
price
was the discount?

7. Joe spent of his money on a pair of shoes and

percentage of his money did he spend?
of the remainder on a pair of socks. What
 $0.50 eauil
Amy had S20.
She bought a pencil box which cost S6.40 and 5 pencils which cost
Shespent $2.10 on lunch. What percentage of her money did she have leff?

chicken rice
160 kg of rice. He gave 20 kg to his mother and used 60 kg for his
9. Mr Tan bought
The remainder was given equally to 5 of his friends. What percentage
of the rice did
business.
each friend receive?

area of the garden occupied by the pond

to the
10. There is a pond in a garden. The ratio of the is not
area not occupied by the pond is
7:13. What percentage of the area of the garden
occupied by the pond?

Word Problems (1) Practice 6.2

Solve the following word problems. Show your working clearly.
1 dress which cost S120. How much money did she haveat
Jen spent 40% of her money on a
first?

8S
 42% of the cost. IfIf James
James
James and Linda shared the
cost of a dinner. Linda paid paid S69.60.
2. the dinner?
how much was the cost of

3. Philip paid $1551.50 for a plasma television including 7% GST on the price of the plasma
television. What was the price of the plasma television before GST?

44. Samuel had some money. He spent $196 on a pair of running shoes. He spent 40% of his
remaining money on a sweater which cost $32. How much money did he have at first?

55 The temperature
of a
the water increased bykettle
of water was 28 °C. Affer
63%. heating for 2 minutes, the temperature of
(a) What was the increase in the
(b)What was the temperature of temperature of the water?
the water after
heating for 2 minutes?
 Last month, the price of an MP3 player was $40. This month, the price of the MP3 player
3
increased by 20%. Judy bought the MP3 player this month. How much did she pay tor tne
player?

7. Don's allowance for November was $165. His allowance for December was reduced by 15%.
How much allowance did Don receive in December?

Joshua spent $150 on Saturday. On Sunday, he spent $225. What was the percentage increase
8.
in the amount of money he spent from Saturday to Sunday?

9 In January, Mr Ong earned $3500. In February, he earned $3050. What was the percentage
to Express your answer correct to
decrease in the amount he earned from January February?
1 decimal place.

$7
 10 such watches
The usual price of a watch was S120. During a sale, y paid S160 for 2 such
watches. What
the percentage discount? wos

Word Problems (2)

Practice 6.3
Solve the following word problems. Show your working clearly.
1. The cost of a haircut is 40% less than the cost of a perm. The cost of a haircut is S18.
Find the
cost of a perm.

2. The total cost of 5 bowls of salad is $16. Apizza costs 50% more than the 5 bowls of salad. Finc-
the total cost of the 5 bowls of salad and the pizza.

3. Last year, the population of Town A and

vear, the population of Town A increasedtheby population
of Town B were in the ratio
32%. If the total 5:6. Ihis
iast year was 385 000, whaf was the population of Town A this population of Town A and Tow
year?
 When a number is Increased by 40% and then reduced by 60%, the result is 42. What is fhe
original number?

5. Brandon and Julian shared a sum of money. If Julian received $54 more, the amount of
money Brandon received would decrease by 30%. Find the original amount of money Brandon
received.

6. Jason and Lynn shared the cost of a meal. James paid $72. If he paid $24 less, the amount
that Lynn paid would increase by 80%. What was the cost of the meal?

7. In January, James saved $360. Florence saved as much as James. In February, Florence
saved 20% less than in January. How much did Florence save in February?
 his
income towife. His May wos
income in May was 35%
less
26%

gives 80%of his monthly

money he gave to his wife was S840
8.
8 . Philip always the
As a result,
amount of less.
than his income in April.
What was his income April?
in

less than each

sold at $10 each. Each Grade B durian cost 20%
Grade A durians were
Grade B durians. The ratio of the
Grade A durian. Alfred paid $470
for some Grade A and
number of Grade B durians
he bought was 7:3.
number of Grade A durians to the
did he buy?
(a) How many Grade A durians than on Grade B durians?
How much more money did he spend on Grade A durians
(b)

less than an adult

10. Adult tickets for a concert were sold at $80 each. A child ticket cost 25%
ticket. On a certain day, the total sales tickets amounted to $28 500. If of
the tickets sold
of
were adult tickets, find the total amount collected from the sale of the adult tickets.
 Revision6
following word problems. Show your working clearly.
Sove the
What percentage of the square shown is not shaded?

25 Cm cm

12 cm
25 cm

The usual price of a handbag was $660. Duringa sale, Jane paid $561 for the handbag.
2 What was the percentage discount?

3 . Acup of hot coffee was left on the table. After 5 minutes, the temperatureofthecoffe
decreased by 15% to 68 °C. After another 15 minutes, the temperature of the coffee decreased
further by 55%.
a What was the temperature of the cup of coffee at first?
(6) What was the temperature of the cup of coffee after 20 minutes?

91
 coin bank are fifty-cent coins. ainder are
ofthe remainder are ten-cent
coins and
coie
4. of the coins in a the
rest are twenty-cent coins.
(a) What percentage of the coins are twenty-cent coins?
bank, how many coins are there altoe
b) If there are 120 twenty-cent coins in the coin
the coin bank?
together in

musical failed. Out the children

of failed, 258 of
who
55 . 86% of the children who auditioned for a how
children passed the audition, many boys
them were girls and the rest were boys. If 56
failed the audition?

on a farm. 40% of them were roosters. This month, some

6. Last month, there were 150 chickens
hens decreased by 60%. How many hens were left
hens were sold. As a result, the number of
on the farm?

Mav's score for English in the mid-year examination was 54. The ratio of May's scoreto
7 Alf's SCore for English in the mid-year examination was 3:4. In the end-of-year examination
Alfs score for English increased by z5%. Vvnaf was Alf's SCore for English in the end-of-yea
examination?
 Mr Tan had some money. He gave 80% of the money to his wife, his daughter and 4 SOns
8. His wife, daughter and sons shared the amount of money in the ratio 5:1:6. If eacn son
roceived $210, what was the amount of money Mr Tan had at first?

9. In the year 2008, 60% of the enrolment in a judo class were girls. The rest were boys. 20% of
the girls left the class in the year 2009. If there were 450 boys in the class in the year 2008, how
many girls were there in the class in the year 2009?

10. Sunny bought himself a watch which cost $180. Hebought another watch which cost 30
more than the first watch for his wife. Later, he bought a third watch which cost 60% less than
the second watch for his daughter. How much did he pay for the three watches altogether?
 Topical Review

Section A
For each question, four options are given. Choose the correct answer and write itss m.
number ir
the brackets provided.

Express 180 cm as a percentage of 3.6 m.

(1) 10% (2) 50%
(3) 200% (4 500%

2. 36% of a length of time is 3 hours. What is 60% of the length of time?

(1) 108 min (2 200 min
(3) 300 min (4 500 min
3. Mark scored 45 out of 60 marks for his Chinese test. Find his percentage score for thetest
(1) 0.75% (2) 45%
(3) 60% 14 75%

4.
Apot contained 4 of water. Alice poured out 500 ml of water from the pot. What percentage
of the water did Alice pour out?
(1) 4% (2) 12.5%
13) 20% (4) 125%

5 30% of the pupils in a school are girls. If there are 210 girls, how many pupils are there in the
school?
(1) 700 (2) 490
(3) 420 4) 280

6. There are 42 pupils in a class. 21 of them are boys. What percentage of the pupils in the dlass
are girls?
() 21% (2) 25%
(3) 50% (4) 200%

7. The usual price of a toy was $18. Daniel sold the

toy for $27. Find the percentage increase in the
price of the toy.
(1) 25% 2) 33.3%
(3) 50% (4) 66.6%

8. Neil spent $500 of his salary and had

(1) 33.3%
$750 left. What
(2) 40% percentage of his salary did Neil spend
(3) 60% (4) 66.6%

9. Susan spent 40% of her money on d book. If she had

$24 left, how much did
first? Susan havea
(1) S80 (2 $60
(3) $40 4 $20

10. A sofa was sold at $2100. s original price was S2800. What was the
(7 10% (2) 15% percentage discount
13) 25% 14) 33.3%
 section B
Write your answers in the spaces
answers in the units stated. provided. For questions which
require units, give your
11 Mr Tan bought a computer at $2400. This was 80%
discount? of its usual price. How much was the

12. 630 people took part in a marathon.

63
What percentage of the people were of them were men and the rest were women.
women?

13. Seth bought a bag at a discount of 25%. If she paid $60 for the
of the bag? bag, what was the usual price

5.
14 The price of a kilogram of
prawns was $24 on Sunday. The price of a
What was the percentage decrease inkilogram
of prawns was $21 on of the same type
Monday.
of the prawns from Sunday to the price of a kilogram
Monday?

15. A number, X, is 40% less than another number, Y. If the number Y is

150, find the number X.

16. The room temperature was 32 °C in the afternoon. In the

decreased by 5%. What was the decrease in the room evening,
the room temperature
temperature?
C

17. In a school, there were 2000 pupils. There were 300 more girls than boys in the school. What
percentage of the pupils were boys?

18. David spent 42% of his money on a book and 28% of it on a pen. He had $4.80 left. How much
money did he have at first?

$.
19.of
the members of a first-aid club were Chinese. 2 of theremainderwere Malays and the
rest were Indians. What percentage of the members were Indians?

20. Martha savedan equal amount of money each day from Wednesday to Saturday. The total
amount saved was520.on Sunday, she saved S6. What was the percentage increase in the
amount she saved from Saturday to Sunday?

%
 Girls

After
1200
Boys
Girls ?

1 unit
5 units
1200 pupils
> 1200 x 5
= 6000 pupils
XYZ School had 6000
pupils in February.
Topic 6 Percentage
Practice 6.1
1 Selling price48000
Original price60
000
48000 100%
60000 80% =

The selling price was 80% of the

original price.
2. Fraction of money that
was left after buying the dress = 1-

1-

Fraction of money that was left in the end =

x
20

235
 Percentage of money left = x 100% 9 Mass of rice given to friends = 160- 20-60
20 = 80 kg
= 35% Mass of rice given to each friend 80 5
She had 35% of her
money left. 16 kg
3. Total area Percentage of rice each friend received = x 100%
occupied by playground and pond =100
550+550
m2 10%
Area occupied by playground and Each friend received 10% of the rice.
Area of land pond
4400
Percentage of land occupied by playground and pond 10. Number of units representing the area of the garden =7+13
4400 100%
Fraction of the area of the garden that is not 20
25% occupied by the
25% of the land is
occupied by the playground and the pond pond 20
together. Percentage of the area of the garden that is not
occupied by
4. la) Fraction the pond= x 100%
of toys that are not stuffed toys =1-
= 65%
65% of the area of the garden is nof occupied by the pond.
Percentage of toys that are not stuffed toys = x 100% Practice 6.2
75% 1. 100
75% of the toys are not stuffed toys.
A0
(hl
(D) Number oftoy robots
Total number of toys 8 $120

Percentage of toys that are toy robots = x15 100%

500
40%> $120
= 23%
Percentage of toys that are not stuffed toys or toy robots 10% $120 4
= 75% - 23% $30
= 52% 100%> $30 x 10
52% of the toys are not stuffed toys $300
or toy robots. She had $300 at first.
5. Total amount given to the three children $20 + $48 + $52 2.
$120 Percentage of the cost that was paid by James
Amount Tim received 48 100% -42%
Total amount 120 58%
48 100% =40% 100%
Tim received 40% of the total amount of 58%
three children.
money given to the
$69.60
6. Discount = $2000 - $1600
$400
Discount 400 58% $69.60
Original price 2000 1% $69.60 58
= $1.20
2000x 100% = 20%
100%> $1.20 x 1000
The discount was 20% of the original price. $120
The cost of the dinner
7. Fraction of money left after buying shoes =1- was $120.
3.
100%+7% =107%
Fraction of money spent socks
107%$1551.50
on =
x 1% $1551.50 107
= $14.50
100%» $14.50 x 100
Fraction of money spent =

The
$1450
price of the plasma television before GST was $1450.
4. 40% of his
9
10% of his
remaining money $32
remaining money » $32 + 4
Percentage of money that was spent $8
x 100% 100% of his
45%
remaining money $80 x 100
He spent 45% of his money. $80

8. Total cost of pencils = $0.50 x 55

$196+$80 $276
He had $276 at
first.
= $2.50
Total amount spent = $6.40 + $2.50 + $2.10 . a) Increase in
$11
temperature = 63% of 28
Amount left = $20 - $11 63 x 28
= $9 = 17.64 °C
Percentage of money left = 2 x 100% he increase in the temperature of the water was
17.64 °C.
=:45%
She had 45% of her money left.

236
 (b) 28+ 17.64 =45.64
3. Town A
The temperature of the water after heating for 2 minutes
was 45.64 °C. 385 000
Town B

6. Increase in price
= 20% of $400
Total number ofunits =5+6
= 06x$400 = 11
$80 11 units 385 000 people
$400S80 $480 1 unit 385 000 11
She paid $480 for the MP3 player. = 35 000 people
5 units 35 000 x 5
7. Reduction in his allowance 15% ofS165 = 175 000 people (popu tion of Town A)
=O x$165
100
Increase in population of Town A 0x 175 000
$24.75
= 56 000
$165 $24.75 $140.25
Don received $140.25 in December. 175 000+ 56 000 231 000
The population of Town A this year was 231 000.
8. Increase in amount spent = $225-$150
$75 4. Work backwards.

50x 100% = 50% 100%

The percentage increase in the amount of money he spent Number after increase
was 50%.
Result 42 60%
9. Decrease in the amount earned = $3500 - $3050
= $450 100% 60% = 40%

S0x100% = 12.9% 40% 42

10% 42 + 4
The percentage decrease in the amount he earned was 10.5
=

12.9%. 100%> 10.5 x 10

105
10. Amount she paid for each watch = $180 + 2 The number becomes 105 after the increase.
$90
Discount = $120 - $90 100%

530 Number 40%

90x 100% = 25%
Number after increase 105
The percentage discount was 25%.
100% + 40% = 140%
Practice 6.3
. 140%> 105
100%
10%> 105 1 4
Perm 7.5
100% » 7.5 x 10
Haircut $18 40% 75
The original number is 75.
100% 40% = 60%
5. 100%
60%
10%
$18
$l8 6 Amount Brandon received
$3
100%> $3 x 10
= $30 30%,
S54
The cost of a perm is $30. 30% $54
10%> $54 + 3
2. 100% $18
100% $18 x 10
5 bowls of salad $16 50% $180
The original amount of money Brandon received
Pizza
was
$180
6. 100%
100% +50% = 150%
Amount Lynn pald| 80%
100%> $16
10% $16 + 10 $24
= $1.60
150%> $1.60 x 155 80%> $24
$24 10%> $24 + 8
$3
$16 +$24 = $40 100%> $3 x 10
The total cost of the 5 bowls of salad and the pizza is $40
= $30

$72+ $30 $102

The cost of the meal was
$102

2
 7. 100%0
$360 10
James'
in Jan
savings Adult ticke $80

Florence's
savings in Jan Child ticket 25%
Florence's
Savings in Feb 20% 100%-25% = 75%

Cost of a child ticket = 00 x $80

Amount Florence saved in January $60
=x $360
$280 Number of adult tickets: Number of child tickets
4 5-4
100% 20% = 80%
4
100% S280
10% $280 10 Total cost of 4 adult tickets and 1 child ticket
$28 = 4 x $80 +1x $60
80% S28 x 8 $380
$224
Florence saved $224 in Number of groups of 4 adult tickets and 1 child ticket sold
February. = $28 500 $380
= 75
100%
Amount given to wife Number of adult tickets sold = 75 x 4
in Apr = 300
Amount given to wife| 300 x S80 = $24 000
in May 35% The total amount collected from the sale of the adult tickets
$840
was $24 000.
35% $840
1% S840 35 Revision 6
$24 1. Area of square = 25 x 25
100% $24 x 100
= $2400
625 cm2
Area oftriangle = x 12 x 15
80%

Income in April $2400

90 cm2
Area of square that is not shaded = 625-90
100%, ? = 535 cm2

80% $2400 Percentage ofsquare that is not shaded = x 100%

10%> $2400+ 8 85.6%
$300 85.6% of the square is not shaded.
100% S300 x 10
$3000 2. Discount = $660 - $561
His income in April was $3000. $99
9 a) 100%
Percentage discount 60 x 100%
Cost of Grade A durian S10
15%
The percentage discount was 15%.
Cost ofGrade Bdurion
20% 3 a) 100%
100% 20% = 80% At first

Cost ofeach Grade B durian = o x $10 After 5 min 68 °C 15%

00
=S8
Total cost of 7 Grade A durians and 3 Grade B durians
100%-15% = 85%
7 x $10 +3 x S8 85% > 68 °C
$94 1% 68 + 85
Number of groups of 7 Grade A durians and 3 GradeB = 0.8 °C
durians bought = $470 $94 100%> 0.8 x 100
= 5
80 °C
The temperature of the cup of coffee at first was 80 °C.
7x5 35
He bought 35 Grade A durians.
(b 100%
b) Amount spent on Grade A durians = $10 x 35 After 5 min 68 °C
$350
Amount spent on Grade B durians = $470 $350
After 20 min 55%
$120
$350-$120 = $230
100%- 55% =45%
He spent $230 more on Grade A durians than on Grade
B durians. 100% » 68 °C
1%> 68 + 100
= 0.68 °C

45%»0.68 x45
30.6 °C
The femperature of the
cup of coffee after 20 minutes
Was 30.6 °C.

238
 atty-centcOins
en-cent coins twenty-cent coi 100%» 772
1%72 100
.72
125%0.72 x 125
From the model, 90
Fraction of coins that are twenty-cent coins 20 Ali's score for English in the end-of-year examination was 90.

8. Total amount his 4 sons received $210 x 4

$840
Percentage of coins that are twenty-cent coins
Total number ofunits =5 +1+6
100% 12
40% 6 units $840
40% of the coins are twenty-cent coins. l unit > $840 6
$140
b) 40% 120 coins 12 units $140 x 12
10% 120+4 = $1680
30 coins 80% $1680
100% 30 x 10
10% $1680 8
300 coins $210
There are 300 coins altogether in the coin bank.
100% $210 x 10
100% $2100
The amount of money Mr Tan had at first was $2100.
56
86% 9. Inthe year 2008,
Percentage of children who passed the audition 100%
= 100% - 86%
450
14%
60%
14%56 children 100% 60% = 40%
1% 56 14
= 4 children 40% 450 children
86% 4x 86 10% 450 4
= 344 children = 112.5 children
60%> 112.5 x 6
344 258 =86 = 675 children lgirls)
86 boys failed the audition.
100%
6. Percentage of chickens that were hens = 100% - 40%
In 2008 675
= 60%

Number of hens on the farm last month = 00x 150 In2009 20%
100%-20% = 80%
90
100% 100%675 girls
10% 675 10
Lastmonth 90
67.5 girls
80% 67.5 x 8
This month 60% = 540 girls
There were 540 girls in the class in the year 2009.
100% - 60% = 40%

10. 100%
100%»90hens
10% 90 10 First watch $180 30%
= 9 hens
40%> 9 x4
= 36 hens
Secondwatch ?

36 hens were left on the farm. 100%+30% = 130%

7. 100%> $180
54
10% $180 + 10
May $18
130%> $18 x 13
Ali $234
100%
3 units 54 Second watch $234
1 unit> 54 3
18 Thirdwatch ? 60%
4 units 18 x 4
72 100% 60% = 40%
100% 100%> $234
10%> $234 10
Mid-year examination 72 25% 23.3.40
40%> $23.40 x 4
End-of-year examination 3.60
100%+25% =125% $180+$234 + $93.60 = $507.60
He paid $507.60 for the three watches altogether.

239
Topical Review
Section A
1. (2) 2. (3) 3 (4) 4. (2) 5 (1)
6. (3) 7. 13) 8. (2) 9. (3) 10. (3)
Section B
11. 600 1290 13. 80 14. 12.5 15. 90
16. 1.6 17. 42.5 18. 16 19. 21.25 20. 20
SectionC