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/ 48
Chapter 9 Percentage
Notes For Pupils
In this chapter, it must first be understood that percentage is just another form of
fraction or ratio. For example, if John has 3 as many marbles as Mary, in ratio it will
be expressed as ‘the ratio of John’s marbles to Mary's marbles is 1:2’. In percentage, it
will be expressed as ‘John has 50% as many marbles as Mary’.
Another important aspect of percentage is to understand the language used in word
problems. The 3 expressions of percentage are ‘more than’, ‘less than’ and ‘as much
as’. An important point for pupils to note is ‘unless the original base is 100% or the
same’, one percentage cannot be added or subtracted from another percentage
directly.
1 NSN
Example
A shirt in Shop X sells for $25. A similar shirt in Shop Y cost 20% more. How much
does it cost in Shop Y?
Since the shirt in Shop Y cost 20% more
than the shirt in Shop X, the cost of the
shirt in Shop X will be the base (100%).
When the phrase ‘more than’ is used,
the resulting percentages will be 100%
Shirt in Shop X cost 100%
Shirt in Shop Y cost 120%
Shirt X 100% — $25
4% — $25 +25
= $1 and above.
Cost of shirt in Shop Y > 120%
+ 30x $4
= $30 E
The shirt in Shop Y costs $30 . : ss
oa
Try the following questions based on the example in 9.1.
Construct: More Than In Percentage
4. Ramesh is 40% heavier than Lionel. If Ramesh is 49 kg, find the weight of Lionel.
Visit www.onsponge.comfor solutions and more! Page 165 Name _ Class Date
Construct: More Than In Percentage
2. A calculator in Pioneer Bookstore cost $16, which was 25% more than the cost in
Selegie Bookstore. How much did the calculator cost in Selegie Bookstore?
3. Jason and his two friends ordered $60 worth of food at a restaurant. A service
charge of 10% was added to the bill. How much did each person have to pay if they
shared the bill equally?
Forfull solution, visit
x 120 + phrase ‘less than’ is used, the
10% — 130 10 percentages will be 100% and below.
Total — 170%
= 17x12
= 204
They have 204 marbles altogether. =m,
\
“a |
Try the following questions based on the example in 9.2.
Construct: Less Than In Percentage
1. Ramesh has 150 stickers which is 25% lesser than Charles. How many stickers
does Charles have?
thinkingMath @onSponge
Page 168 Name : Class : Date :
Construct: Less Than In Percentage
2. A notepad cost 15% cheaper in the school bookshop compared to the estate
bookstore. Given that the price difference is 90 cents, calculate the cost of the
notepad in the school bookshop.
3. Mr Lim was informed that he would be receiving a 20% cut in his salary due to
recession. Given that the deduction amounts to $800, how much was his old
salary?
4. At a party, there are 50 more women than men. The number of men is 75% as
much as the women. How many people are there at the party?
Forfull solution, visit
a .www.onsponge.com
Visit www.onsponge.com for solutions and more! Page 169 Name: Class Date :
Construct: Less Than In Percentage
5. In a bag made up of green and blue balls, there are 30% as many green balls as
blue balls. How many green balls are there in the bag if there are 28 more blue
balls than green balls?
Forfull solution, visit
3 -www.onsponge.com
\
6. Abag consists of some 20-cent and 50-cent coins, there are 85% as many 20-cent
coins as 50-cent coins. How much money is there in the bag if there are 30 more
50-cent coins than 20-cent coins?
In a class, there are 25% as many boys as girls. How many percent more girls
than boys are there?
as
Forfull solution, visit
% .www.onsponge.com
thinkingMath@onSponge
Page 170 E KEY CONSTRUCT: MULTIPLICATION IN PERCENTAGE
Example
Mrs Lim’s salary was 30% less than her husband. After Mrs Lim had a pay raise of
10%, she earned $460 less than her husband. Find the salary of Mrs Lim in the end.
At first,
Mrs Lim 70%
Mr Lim 100%
Percentage raise in Mrs Lim’s salary > 10% of 70%
~ 1x 70%
10
= 7%
Since Mrs. Lim earned
30% less than her
husband (base), Mrs.
Lim's initial salary will be
70%. Mrs. Lim's pay
increase of 10% cannot
be added — directly
because her original
salary is not 100%.
Therefore the effective
increase is actually10%
In the end,
Mrs Lim 70% + 7% =77%
Mr Lim 100%
Difference in salary + 100% — 77% = 23%
23% — $460
1% — $460 + 23
= $20
Salary of Mrs Lim — 77% x $20
= $1540
Mrs Lim earned $1 540 in the end.
Note: Unless the original percentage is the base (100%), one percentage cannot be
directly added or subtracted from another percentage. To find the effective increase or
decrease in percentage, first calculate the product of increase or decrease in
percentage and the base or original percentage.
Visit WWwW.onsponge.com for solutions and more! Page 171 Name Class : Date
Try the following questions ‘on the example in 9.3,
Construct: Multiplication In Percentage
1. Janice’s savings is 20% more than David's savings. If Janice’s savings is
decreased by 20%, their total savings will be $980. How much is Janice’s savings
at first?
2. Mr Singh always gives 30% of his income to his wife. When his income is
increased by 20%, he gives her $240 more. Find his income before the
increase.
3. Kenneth saves 45% of his salary. When his salary is reduced by 20%, his
savings is reduced by $90. How much is his salary at first?
+hinkingMath@onSponge
Page 172 Name =
Class : Date :
Construct: Multiplication In Percentage
4. A tank was 60% full of water. When 40% of the water was used, 72 litres of water
remained in the tank. What was the capacity of the tank?
5. There are 25% more red marbles than blue marbles in a bag. After | removed 40%
of the red marbles and increase the number of blue marbles by another 10%, there
is now 70 lesser red marbles than blue marbles. Find the number of blue marbles
at first,
6. Muthu’s salary was 10% less than Esther. After Muthu had a pay raise of 20% and
Esther had a pay cut of 20%, Muthu's salary was $560 more than Esther's. Find
the salary of Muthu in the end.
Visit www.onsponge.com for solutions and more! Page 173 Name : Class Date :
Construct: Multiplication In Percentage
7. A school library had 3 900 books. The number of Chinese, Malay and English
books is in the ratio 4:3:6 respectively. When the school bought 510 new books, the
number of Chinese books increased by 20% and the number of Malay books
increased by 10%. Find the percentage increase in the number of English books.
Forfull solution, visit
5 .www.onsponge.com
iS
8. The ratio of Vernice’s weight to that of Nathaniel’s weight was 3 : 4. If Vernice’s
weight were to increase by 40%, by what percentage must Nathaniel’s weight be
increased or decreased so that their weight would be the same?
9. A rectangle is 25 cm long and 20 cm wide. Its length is now increased by 40% and
its breadth is increased by 50%, find the perimeter of the new rectangle.
thinkingMath@onSponge
Page 174 Name : Class Date
Construct: Multiplication In Percentage
10.A rectangle measures 20 cm by 16 cm. Its length and breadth are both increased
by 25%. Find the percentage increase in its area.
Forfull solution, visit
a www.onsponge.com,
11. Mrs Ismal always spends 80% of her salary. Her salary for April was 20% less than
that for March. As a result, her expenditure in April decreased by $640. What was
Mrs Ismal's salary in April?
142.Mr Lim always spends 75% of his salary. His salary for May was 20% more than
that for April. As a result, his expenditure in May increased by $450. What was his
salary in May?
Forfull solution, visit
s wwww.ensponge.com
N
Visit www.onsponge.comfor solutions and more! Page 175 eee OVERLAPPING PERCENTAGE
Example
Some pupils went to watch a play and a musical. Some went only to the play or only to
the musical, and some went to both. 75% of the pupils went to the musical, and 80% of
the pupils went to the play.
(a) What percentage of the pupils went to both the play and the musical?
(b) If 40 more pupils went to the play only than to the musical only, how many pupils
went to both the play and the musical?
At first,
Pupils who watched play — 80%
Pupils who watched musical — 75%
Total percentage initially + 80% + 75% As the total of
= 155% the percentages
(75% + 80%)
(a) Percentage of pupils who went to both the musical and play —— a ae eS
155% —100% the two groups
= 55% that overlaps.
This group of
. jis went to
(b) Percentage of pupils who went to play only ey etal
— 80% -55% and play.
= 25%
Percentage of pupils who went to musical only
— 75% — 55%
= 20%
Difference in percentage of pupils who went to musical and play oe
+ 25% — 20% vad
= 5%
5% — 40
1% > 4075
=8
Number of pupils who went to both musical and play — 55%
55 x8
= 440
440 pupils went to both the musical and play.
ae +thinkingMath@onSponge Name : Class : Date :
Try the following questions based on the example in 9.
Construct: Overlapping Percentage
4. Ina streaming exercise, pupils were asked to choose 2 subjects, which was Grade
‘A Math or Grade B Math. 80% of the students chose Grade A Math, 35% of the
pupils chose Grade B Math and 10% of the pupils chose neither subjects. Given
that a total of 75 pupils actually chose both Grade A and Grade B Math, how many
pupils were involved in the streaming exercise?
2. Ata funfair, the kids can choose to sit for a ride at the Mary-Go-Round and or the
Too-too train with their complimentary coupons. 70% of the kids went for the Mary-
Go-Round, 45% went for the Too-too train, but 10% of the kids did not go for any of
the 2 rides. Given that a total of 75 kids went for both rides, how many kids did not
go for any of the 2 rides?
Visit www.onsponge.com for solutions and more! Page 177 Name Class : Date
Construct: Overlapping Percentage
3. During a school survey, some pupils were asked to choose whether they like
badminton and or table-tennis. 65% of the pupils chose badminton, 75% of the
pupils chose table-tennis and 5% of the pupils did not choose any of the 2 sports.
Given that a total of 90 pupils chose both badminton and table-tennis, how many
pupils were involved in the survey?
4. A group of 200 pupils were interviewed to find out whether they enjoy
swimming, jogging, swimming and jogging, or neither of the two sports. 82% of the
pupils indicated that they liked swimming, 54% of them indicated that they liked
jogging and 16% indicated that they did not like any of the two sports. How many
pupils enjoyed both swimming and jogging?
Forfull solution, visit
x -www.onsponge.com
\
+thinkingMath@onSponge
Page 178 ER SA a Oe)
Example
If Cheryl sells a watch at a discount of 10% of the usual price, she will make a profit of
$30. If she sells it at a discount of 30%, she will incur a loss of $10. Find the cost
price of the watch
In percentages
At first, involving loss and
Sells at 10% discount > sell at 90% of the usual selling price | profit it willbe
Sells at 30% discount — sell at 70% of the usual selling price | important to
Difference in the selling price > 20% — $30 + $10 remember what
20% — $40 each term means.
. Profit refers to the
1% — $2 money made while
loss is the money
Cost price of watch + 90% ~ $30 or 70% + $10 lost; both are found
— 90 x 2- $30 or 70 x2 + 10 by calculating the
= $150 differences between
the selling and cost
prices,
The watch cost $150.
Try the following questions based on the example 9.5.
Construct: Profit And Loss
4. If Kim Hock sells a collectable toy at a discount of 20% of the usual price, he will
make a profit of $40. If he sells it at a discount of 40%, he will incur a loss of $45.
Find the cost price of the collectable toy.
Visit www.onsponge.com for solutions and more! Page 179 Name Class Date
Construct: Profit And Loss
2. If Tommy sells a book at a discount of 10% of the usual price, he will make a loss
of $15. If he sells it at a discount of 30%, he will incur a loss of $60. Find the cost
price of the book.
3. If Mr Lim sells a washing machine at a mark-up price of 10% above its usual selling
price, he will make a profit of $500. If he sells it at a discount of 20% of its usual
selling price, he will incur a loss of $100. Find the cost price of the washing
machine.
+thinkingMath@onSponge
Page 180 Name : Class : Date
Construct: Profit And Loss
4. \f Rakesh sells a collectable figurine at a discount of 5% of the usual price, he will
make a profit of $75. If he sells it at a discount ‘of 20%, he will still make a profit of
$30. Find the cost price of the collectable figurine.
Forfull solution, visit
www.onsponge.com
5. If Jessica sells a puzzle at a discount of 10% of the usual price, she will make a
profit of $40. If she sells it at a discount of 30%, she will still make a profit of $10.
Find the cost price of the puzzle.
Visit www.onsponge.com for solutions and more! Page 181 9.6__ KEY CONSTRU: PART-WHOLE RELATIONSHIP.
Example
Daniel spent 20% of his money on a pack of cartoon cards. He spent 75% of the
remaining money on a game cartridge.
(a) What fraction of his money was left?
(b) If he was left with $9, how much money did Daniel have at first?
Method 4 (Model Method)
20% — z and 75% — 3
© total Remainder
«og *?7
8
cards Game cartridge left
| 1 Recall what was covered under
(a) Fraction of money left = — the chapter on __ fractions.
5 Whenever a percentage does not
9
represent the whole but what is
1 remaining behind or left behind,
(b) e total — $9 the word problem can be
classified under —Part-whole
Total at first > 5 x $9 Concept. When the model can be
= $45
easily divided, the Model Method
may be suitable. Otherwise, the
Branch Method is a good
alternative.
thinkingMath@onSponge
Page 182 Alternatively, problems involving the Part-whole Concept can also be solved using the
Branch Method.
Method 2 (Branch Method)
4 (cartoon cards) By multiplying the
fractions together, the
5 5 20
fraction that is
4412 representing the whole
NX 5 20
3 3
Total 2 | 2xz= tric called the final fraction
or vw a* 20 (game cart ne) can be calculated. For
12
4 example, 55 means
BN that 12 parts out of the
4 14.4 entire total (20 parts)
(Remainder) — —x— = — (left) was spent on the game
4 45 20 cartridge.
4_1
(a) Fraction of money left > >~ = =
20 5
(b) + total $9 mF
5 <>
Total at first + 5 x $9 \'
= $45 ova |
Try the following questions based on the example in 9.6.
Construct: Part-whole Relationship
1. Ramesh spent 30% of his money on a box of biscuits. He spent 70% of the
remaining money on some donuts.
(a) What fraction of his money did he spend on the donuts?
(b) If he was left with $4.20, how much money did Ramesh have at first?
Visit www.onsponge.com for solutions and more! Page 183 Name Class : Date
Construct: Part-whole Relationship
2. Sharon spent 65% of her money on some cookies. She spent 80% of the remaining
money on a box of crayons and the remaining $14 on a storybook.
(a) What fraction of her money was spent on the storybook?
(b) How much money did Sharon have at first?
3 Dinesh spent 60% of his money on some books. He spent 25% of the remaining
money on a box of paint and 50% of what was left on some magazines.
(a) What fraction of his money was left?
(b) Given that the books cost $36 more than the magazines, find the sum of money
Dinesh had at first.
Forfull solution, visit
4 —
a 10 5
sys PR (each box cut into 2 parts)
cris RT difference (each box cut into 3 parts)
To makes the boxes the same
sizes, the model representing boys
is divided into 2 equal parts each
0 35 +35 10 parts for boys is now
subdivided into 20 parts. For the
girls, the 5 parts is sub-divided into
15 parts. The shaded portion
represents the part of the fraction
that is equal
Total» 35[ ] — 35 pupils
= 1 pupil
Difference between boys and girls > 5{]
5x1
= 5 pupils
There are 5 more boys than girls at the gathering
Method 2
Using the Unitary Method, instead of
3 2. drawing a model, we use the concept of
qo = Bans equivalent fractions and make both the
numerators the same. Comparing with
S boys + © gins the above model, you will realize that the
aan boys 8 anita new fraction of wie Tovincides with
Total girls — 15 units the model above as well. However, it is
Total pupils 35 units > 35 \ far more efficient and saves more time.
unit +1
Difference between boys and girls 5 units E &
5x1 P.
=5 \
“var
+hinkingMath@onSponge
Page 190 Name : Class : Date :
Try the following questions based on the example in 9.7. i
Construct: Equal Fractions
4. 45% of Calvin’s stickers is equal to 25% of Brian's stickers. If Brian has 32 more
stickers than Calvin, what is the total number of stickers Calvin and Brian have?
2. Joanna had $125 more than Kelvin. Joanna spent 65% of her money and Kelvin
spent 40% of his money. In the end, Kelvin and Joanna had the same amount of
money left. Find the amount of money Joanna had at first.
Visit www.onsponge.com for solutions and more! Page 191 Name Class : Date :
Construct: Equal Fractions
3. At the school hall, there were 510 lesser boys than girls. After 60% of the boys and
90% of the girls left the hall for recess, there was an equal number of boys and girls
that remained inside the hall. Find the total number of pupils remaining in the hall in
the end.
Forfull solution, visit
5 jww.onsponge.com
4. Rahim had $85 more than Carena. Rahim spent 90% of his money and Carina
spent 60% of her money. In the end, Carena had twice as much money as Rahim.
Find the amount of money Rahim had at first.
+hinkingMath(@onSponge
Page 192 Name : Class : Date :
Construct: Equal Fractions
5. Mrs Goh baked a total of 350 cheese and chocolate muffins cookies. After giving
away 80% of the chocolate muffins and 75%of the cheese muffins, she was left
with twice as many chocolate muffins as cheese muffins. Find the number of
chocolate muffins that Mrs Goh gave away.
Forfull solution, visit
4 wwwi.onsponge.com
6. There were 90 more boys than girls at a school funfair. After 80% of the boys and
30% of the girls left the funfair, there were twice as many girls as boys left behind.
Find the number of pupils at the funfair at first.
Visit www.onsponge.com for solutions and more! Page 193 eee EXTERNAL UNCHANGED
Example
In a basket, 40% are oranges and the rest are apples. After | gave away 15 oranges,
the oranges will drop to 20%. How many apples and oranges are there in the basket
altogether in the end?
In using the Unitary Method,
instead of drawing a model, the
concept of equivalent fractions is
used and this makes the number
of units for apples the same
since the number of apples
remains unchanged
Method (Unitary Method)
40% — 2 and 20% > +
5 5
Oranges 2 units (40%) x 4 — 8 units
Apples 3 units (60%) x 4 — 12 units
Oranges 1 unit (20%) x 3 3 units
Apples 4 units (80%) x 3 12 units
Therefore, after making the units (apples) the same,
Decrease in oranges — 5 units + 15
1 unit 15+5
= 3
Total fruits left + 15 units
> 15x3
= 45
There are 45 fruits in the basket in the end.
+hinkingMath@onSponge
Page 194 Name : Class : Date
‘Try the following questions based on the example in 9.8.
Construct: External Unchanged
4. Ina class, 60% are boys. After 5 girls leave the class, the percentage of girls will
decrease to 30%. How many pupils are there in the class in the end?
2. Ona bus, there were 40% as many children as adults. After 22 adults alighted from
the bus, the percentage of children increased to 60%. How many children were
there in the bus?
Forfull solution, visit
4 www.onsponge.com
Visit WWw.onsponge.com for solutions and more! Page 195 Name : Class : Date :
Construct: External Unchanged
3. If | add another 40 lemons into a basket of fruits, the percentage of lemons in the
basket will increase from 30% to 50%. How many lemons do | have in the basket at
first?
4. A telematch took place among a group of boys and girls. Midway, another 20 girls
joined in the telematch and the percentage of girls will increase from 40% to 55%.
How many boys were at the telematch?
Forfull solution, visit
x -www.onsponge.com
+thinkingMath @onSponge
Page 196 Example
ads Na
Jenny has 25% as many stickers as Melissa and 20% less stickers than Bernard. If
they have a total of 125 stickers, how many stickers does Jenny have?
Method (Unitary Method)
Jenny ‘unit (25%) x4— 4 units
Melissa 4 units (100%) x 4 — 16 units
Jenny units (80%) — —>4 units
Bernard 5 units (100%) — 5 units
Therefore, combining the two, we have:
Jenny — 4 units
Melissa —16 units
Bernard — 5 units
Total — 25 units + 125
1 unit — 125+ 25
=5
Total stickers Jenny has — 4 units
4x5
= 20
Jenny has 20 stickers.
In using the Unitary Method,
instead of drawing a model, the
concept of equivalent fractions
is used to make the repeated
individual (Jenny) the same
units. It is far more efficient and
saves more time
Try the following questions based on the example in 9.9.
Construct: Repeated Identity
1. Ramesh has 30% more cards than Arun and 40% less cards than Jody. If they
have a total of 402 cards, how many cards does Jody have?
Visit www.onsponge.com for solutions and more! Page 197 Name : Class Date :
Construct: Repeated Identity
2. David has 10% less cookies than lan but 40% more cookies than Rauf. If they
have a total of 890 cookies, how many cookies does lan have?
3. Fiona scored 25% higher than Helen but 10% lower than Daniel for an IQ test. If
Daniel scored 28 marks higher than Helen, what was Fiona’s score for the test?
+hinkingMath@onSponge
Page 198 Name : Class : Date
Construct: Repeated Identity
4. There are 40% as many boys as girls and 20% more adults than children at a party.
Given that there are 34 more adults than girls, how many people were at the party
altogether?
Forfull solution, visit
1 unit 8
Number of stickers Tammy had at first + 3 units
3x8
= 24
Tammy had 24 stickers at first.
Try the following questions based on the example 9.10.
Construct: Unchanged Total
4. In an express train, the number of adults is 70% more than the number of children.
After 125 adults had alighted from the express train and 125 children had boarded
the express train, there are now 20% lesser adults than children. How many adults
were there in the express train in the end?
Visit www.onsponge.com for solutions and more! Page 201 Name Class : Date
Construct: Unchanged Total
2. Jacintha wanted to fix her animal puzzle. On the first day, she managed to fix 45%
of the puzzle. On the second day, she fixed another 60 pieces of the puzzle. As a
result, 75% of the puzzle was fixed. How many pieces did the puzzle consist of?
Forfull solution, visit
ww.onsponge.com
3. Moses wanted to fix his Power Ranger puzzle. On the first day, he managed to fix
20% of the puzzle. On the second day, he fixed another 44 pieces of the puzzle.
As a result, the number of fixed pieces became 80% of the unfixed pieces. How
many pieces did Moses’ puzzle consist of?
thinkingMath@onSponge
Page 202 Name Class Date :
Construct: Unchanged Total
4. Gerald was reading a storybook. After a week, he managed to read 40% of the
book. After another two weeks, he managed to read another 60 pages. By that
time, he would have read 80% of the book. How many pages were there in the
storybook?
5. Samuel was reading a storybook. The number of pages he had read was 40% of
the number of pages he had not read. If he reads another 22 pages, he would have
read 60% of the book. How many pages are there in the storybook?
Forfull solution, visit
jww.onsponge.com
Visit www.onsponge.com for solutions and more! Page 203 Name : Class : Date :
Construct: Unchanged Total
6. Three friends Cherie, Daniel and Elias shared a present for their teacher. Cherie
paid 50% of the total share of Daniel and Elias. Daniel paid 30% of the total share
of Cherie and Elias. If Elias paid $32 more than Daniel, how much did the present
cost?
7. Three brothers Gerald, Xavier and Joshua shared a box of cookies. Gerald took
45% of the cookies. Xavier took 25% of the cookies taken by Gerald and Joshua. If
Gerald took 25 more cookies than Xavier, how many cookies did the box contain at
first?
Forfull solution, visit
3 .weww.onsponge.com
+hinkingMath@onSponge
Page 204 9.11 KEY CONSTRUCT: CONSTANT DIFFERENCE
Example
At a funfair, there were 60% as many adults as children. After 40 children and 40
adults left the funfair, there were 40% as many adults as children. How many adults
were at the funfair at first?
Method (Unitary Method)
At first
Adults 3. units (60%) x3 9 units
Children 5 units (100%) x 3 — 15 units
Difference 2 units
In the end
Adults 2 units (40%) x2— 4units
Children 5 units (100%) x 2 > 10 units
Difference 3 units
Since an equal number of adults and children left the funfair, we will make the
difference in units the same.
Decrease in units each — 5 units — 40
dunit > 40+5
= 8
Number of adults at first 9 units
9x8 eg
= 72 >
There were 72 adults at first. Oe! |
Since an equal number of adults and children
left, the difference between the adults and
children before and after the change must
remain the same. As there are two sets of units
and the absence of such phrase “whole
number more than or less than”, the Unitary
Method is preferred. Using the principle of
common multiple, the difference in units before
and after is made the same.
Visit www.onsponge.com for solutions and more! Page 205 Name Class Date :
Try the following questions based on the example 9.11.
Construct: Constant Difference
4. In aclass, 30% were boys. After another 9 girls and 9 boys joined the class, there
were 60% as many boys as girls. How many pupils were there in the class in the
end?
2. Alan had 75% as much money as Kumar. After Alan and Kumar each donated
$400 to charity, Alan had 25% as much money as Kumar. Find the sum of money
Alan had at first.
+hinkingMath@onSponge
Page 206 Name : Class : Date
Construct: Constant Difference
3. There were 1 680 pupils in school X and 20% more pupils in school Y. When an
equal number of pupils left each school, the ratio of the pupils in school X became
60% that of School Y. How many pupils are there in school X in the end?
Forfull solution, visit
x swww.onsponge.com
\
4. Shop X had 4 as many shirts as Shop Y. After both shops sold 75 shirts each,
Shop X was left with 55% as many shirts as Shop Y. Find the number of shirts
Shop X had in the end.
Visit www.onsponge.com for solutions and more! Page 207 Name: Class : Date :
Construct: Constant Difference
5. The figure is made up of two squares of different sizes. The area of the small
square is 40% of the area of the big square. A shaded area a 20 cm? is being
removed. The area of the unshaded smaller square is now i the area of the
unshaded bigger square. Find the area of the smaller square.
Forfull solution, visit
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6. Alexander is 40% as old as his brother. In 21 years’ time, he will be 75% as old as
his brother. How old is Alexander now?
+hinkingMath@onSponge
Page 208 CHANGED.
Example
A box contained some square and round cookies. 40% of these cookies are round.
After removing 55 square and 10 round cookies, the number of square cookies
became 70% as much as the round cookies. How many cookies were there in the box
at first?
“Use a different label for the different sets of ratios (units and parts) to differentiate the
different quantities they represent.
“By making the end ratios (parts) the same, identical models are drawn to
compare the difference in the units.
“» Whenever there is a negative quantity, it is represented on the model of the other
person or quantity.
Square Round -
x10, 2 units (60%) 2 units (40%) Omerat deer ey ae
= 55 —=10_ 7. replaced with parts to represent
7 parts 10 parts the different sizes. Since
(70%) (100%) nothing remains constant in
such problems, the way to
~ solve this type of problem is to
Square | 30 units 10.x7 (Round) make the end (parts) the same
: by use of common multiple. A
Round | ‘units | 55x10 (Square) model representing the ‘same
oun number of parts for each
amount is drawn, From here,
70 parts the different units and numbers
involved can be compared
the length
Therefore, 16 units —» 550-70 eee
1 unit > 480 + 16
= 30
Number of cookies at first + 5 units =
5x30
= 150
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Try the following questions based on the example in 9.12.
Construct: External Changed
4. A box contained some twenty-cent and fifty-cent coins in the ratio 3:4. When
10 fifty-cent coins were taken out and replaced by twenty-cent coins, the ratio
becomes 7:5. Find the sum of money in the box at first.
2. At first, Elias had 45% as many stickers as Ramesh. After Elias bought another
39 stickers and Ramesh bought another 20 stickers, Elias now has 75% as many
stickers as Ramesh. Find the number of stickers that Elias had at first.
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x
paez0 +hinkingMath@onSponge Name : Class : Date
Construct: External Changed
3. Last year, the enrolment of School X was 90% that of school Y. This year, the
enrolment of school X decreased by 220 while that of school Y increased by 200. In
the end, the enrolment of school X is 70% that of school Y this year, what was the
enrolment of each school last year?
4. Daniel's savings was 75% as much as Annabel. After Annabel saved another $40
and Daniel saved another $20, Daniel's savings became 3 as much as Annabel’s
savings. Find Daniel's savings at first.
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Construct: External Changed
5. A farmer had 2 as many chickens as ducks at first. After selling 50 chickens and
8 ducks, he had 25% as many chickens as ducks. How many ducks did the farmer
have at first?
Forfulll solution, visit
5 -