Catholic High School 2010 PSLE Math Prelim Paper 2 Q17

Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

Solution

At first
Daniel ---- 100% + 40%
Brandon ---- 100%
Calvin ---- 1 unit

After Daniel and Brandon each gave 20% of their stickers to Calvin…
Daniel ---- 100% + 40% - (28%)*
Brandon ---- 100% - (20%)**
Calvin ---- 1 unit + (28% + 20% of Dan and Bran --> 80% of 1 unit)#
Hence Calvin --- 1 unit + (48% of Dan and Bran --> 80% of 1 unit)

* 20% of 140% = 28%
** 20% of 100% = 20%
# Cal received 28% + 20% = 48% of (Dan + Bran), which is equal to 80% of Cal's original amount of 1 unit.

80% of 1 unit ---- 48% of total of Dan and Bran
0.8 unit ---- 48%
1 unit ---- 48% divided by 0.8 = 60%

In the end Calvin
1 unit + (48% from Dan and Bran)
= 60% + 48%
= 108%

(Daniel) more than (Calvin) in the end
(140% - 28%)## - (108%)
= 112% - 108%
= 4%
## Danile had 140% at first but gave 28% to Calvin

Daniel had 20 more stickers than Calvin in the end
4% ---- 20
1% ---- 20 divided by 4 = 5

Brandon at first
100% ---- 100 x 5 = 500

Answer: 500 stickers

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Catholic High School 2010 PSLE Math Prelim Paper 2 Q18

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?

Solution

Male ----- 120%
Female ----- 100%

Speakers
Male : Female
8 (parts) : 5 (parts)

Participants
Male : Female
1 (unit) : 1 (unit)

Men ----- 8 parts + 1 unit
Women ----- 5 parts + 1 unit

But since there are 20% more women than men,
Women ----- 5 parts x 120% + 1 unit x 120%
= 6 parts + 1.2 units

Men ----- Women
8 parts + 1 unit ----- 6 parts + 1.2 units
8 parts - 6 parts ----- 1.2 units - 1 unit
2 parts ----- 0.2 unit
1 part ----- 0.1 unit
10 parts ----- 1 unit
or
1 unit ----- 10 parts


(a)
Male Speakers ----- 8 parts
Male Participants ----- 1 unit or 10 parts

Male Speakers : Male Participants
8 : 10
4 : 5

Answer: 4 : 5

(b)
Speakers
Male : Female
8 (parts) : 5 (parts) -- (altogether 13 parts)

Participants
Male : Female
1 (unit) : 1 (unit)
10 (parts) : 10 (parts) -- (before)
- 40 : + 60 -- (40 males left; 60 females joined)
3 (units) : 4 (units) -- (3/4 as many male as females in the end)

(Male) 3 units ----- 10 parts - 40
(Female) 4 units ----- 10 parts + 60

(Female) - (Male)
4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)
1 unit ----- 60 + 40
1 unit ----- 100

(Male after)
3 units ---- 3 x 100 = 300

(Male before)
10 parts ---- 300 + 40 (need to add the 40 who left)
10 parts ----- 340
1 part ---- 34

All speakers
13 parts ---- 13 x 34 = 442

Answer: 442 speakers

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Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q16

Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4:1. As a result, Tricia had 2 and 1/2 times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many sttamps did Lena give to Tricia?

Solution

*** Tricia had 75% fewer stamps than Yanling
----- 25% of 160% is 40%.

# Tricia finally had 2 and half times as many stamps as before
----- 40% x 2.5 = 100%


Tricia's number of stamps increased by
---- 100% - 40% = 60%

Ratio given by Yanling and Lena was 4:1 -----
Y : L
4 : 1
(Total 5 units) ----- 60%

**(Lena gave) 1 unit ----- 60% divided by 5 = 12%
*(Yanling gave) 4 units ---- 4 x 12% = 48%

In the end, Yanling had more than Lena ----- 300
112% - 88% ----- 300
24% ---- 300
1% ---- 300 divided by 24 = 12.5

Lena gave Tricia 12% -----
12 x 12.5 = 150

Answer: 150 stamps

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Another Math Problem Sum

I received another request through email from a reader. Anyone willing to help her out?

==========

Alice, Barbie,Cora and Daylia are given some stickers. The number of stickers Alice has is 25% of the number of stickers the other 3 children have. The number of stickers Barbie has is a third of the number of stickers the other children have, while Cora has half of the number of stickers the other children have. If Daylia has 78 stickers, how many stickers does each of the other children have?

Thank You for taking your time to read this. I appreciate it if you could give me a solution to this problem as soon as possible.

==========

RGS Primary 2009 PSLE Math Prelim Paper 2 Q18

At first, 25% of Kumar's money was the same as 33 and 1/3 % of Lily's money. Lily's father gave her $80 later, while Kumar spent $325. In the end, Lily had 2 and 1/2 times as much money as Kumar.

a) How much money did Kumar have at first?

b) How much money did Lily have in the end?

Solution

(Kumar) 4 units --> 2 parts + 325 (x5)**

(Lily) 3 units + 80 --> 5 parts (x2)**

**Kumar (x5) and Lily (x2) to make both of them 10 equal parts each.

(K) 20 units --> 10 parts + 1625

(L) 6 units + 160 --> 10 parts

(K) 20 units --> 10 parts + 1625

(L) 6 units --> 10 parts - 160

(K) - (L)

20 units - 6 units --> 10 parts - 10 parts + 1625 - (-160)

14 units --> 1625 + 160

14 units --> 1785
1 unit --> 1785 divided by 14 = 127.5

(a)

Kumar at first

4 units --> 4 x 127.5 = 510

Answer: $510

(b)
Lily in the end
--> 3 units + 80
(3 x 127.5) + 80
= 382.5 + 80
= 462.5

Answer: $462.50

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RGS Primary 2009 PSLE Math Prelim Paper 2 Q16

There were some sweets in Boxes X, Y and Z. Box X contained 20% of the total number of sweets in Boxes X, Y and Z. The ratio of the number of sweets in Box Y to the total number of sweets in Boxes X and Z is 2:1. If there are 24 more sweets in Box Y than Box Z, find the total number of sweets in Boxes X, Y and Z.

Solution

Box X --> 20% of total sweets
= 20/100
= 1/5 --> (3/15) of total sweets

Box Y --> 2 units
Box X + Z --> 1 unit
(Total 3 units)

Box Y --> (2 units)/(3 units)
= 2/3 --> (10/15) of total sweets

Z --> 2 units
Y - Z --> 24 sweets
10 units - 2 units --> 24 sweets
8 units --> 24 sweets
1 unit --> 24 sweets divided by 8 = 3 sweets
15 units --> 15 x 3 sweets = 45 sweets

Answer: 45 sweets

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RGS Primary 2009 PSLE Math Prelim Paper 2 Q2

A dress cost $139.95. During a sale, a 20% discount was given. Calculate the sale price of the dress.

Solution

Discount --> 20%
Cost after discount --> 80%

Sale price after discount
--> (80/100) x $139.95 = $111.96

Answer: $111.96

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ACS Primary 2009 PSLE Math Prelim Paper 2 Q17

65% of the animals on a farm were cows and the rest were goats. When 240 more cows and goats were added to the farm, the percentage of cows increased by 20% and the number of goats doubled. How many goats were there on the farm at first?

Solution

At first
Cows --> 65%
Goats --> 35%

Cows 20% more
--> (20/100) x 35% = 13% more

Goats doubled
--> 35% more

Total added
13% (cows) + 35% (goats) --> 240
48% --> 240
1% --> 240 divided by 48 = 5

Goats at first
35% --> 35 x 5 = 175

Answer: 175 goats

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ACS Primary 2009 PSLE Math Prelim Paper 2 Q9

The pie chart below shows the different types of muffins sold in a bakery. A total of 240 muffins were sold.

a) How many banana muffins were sold?
b) If a chocolate muffin cost $1.60, how much did the bakery collect from the sale of chocolate muffins?

Solution

a) (1/4) x 240 = 60

Answer: 60 banana muffins


b)
Cheese --> (1/8) x 240 = 30
Blueberry --> (20/100) x 240 = 48
Banana --> 60
Chocolate Chip --> 68

Total for the above
--> 30 + 48 + 60 + 68 = 206

Chocolate --> 240 - 206 = 34

Sale collected from chocolate muffin
--> 34 x $1.60 = $54.40

Answer: $54.40

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Request for help - CHIJ St Nicholas 2009 Prelim Paper 2 Q17

Hello everyone, I received an email from a reader seeking some help. Below is the email reproduced unedited. Please feel free to help.

======================

Hi,
I am a regular reader of your blog "road-to-psle". I have 1 question from CHIJ St Nicholas 2009 Prelim Paper 2 Q17 that I cannot solve. I have asked many people including tutors and teachers but they also cannot solve. Can you please help me? The question:

At Carpark P. the number of lorries to that of vans was in the ralio 3: 7.
At Carpark Q, the number of lorries to that of vans was in the ratio 8: 9.
When 40% more lorries from an industrial park entered Carpark P and
20% of the vans at Carpark Q moved to Carpark P. there were 76 fewer
Iorries at Carpark P than at Carpark Q. How many vehicles were there
altogether at the two carparks finally? Ans:564

Thanks
John

=====

Please post solutions here.

http://www.atfreeforum.com/excel/viewtopic.php?p=5&mforum=excel#5

CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q15

There were some prizes ot be won at a Shop and Win Contest. 35% were cash prizes and there rest were household items. Some cash prizes were given out and the percentage of cash prizes decreased to 22%. If there were 54 more household items than cash prizes at first, find the number of cash prizes being removed.

Solution

Before
Cash --> 35%
Household Items consists of
--> 35% + 30%(54 items) = 65%

30% --> 54
1% --> 54 divided by 30 = 1.8
(Cash before) 35% --> 35 x 1.8 = 63
(Household Items) 65% --> 65 x 1.8 = 117

After
Cash became --> 22%
Household Items --> (remaining) 78%

78% --> 117
1% --> 117 divided by 78 = 1.5
(Cash after) 22% --> 22 x 1.5 = 33

Cash before - Cash after --> Cash prizes removed
63 - 33 = 30

Answer: 30 cash prizes

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CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q14

There were ducks, goats and hens at a farm. 15% of the animals were ducks. There were 180 fewer ducks than hens. The remaining 121 animals were goats. What percentage of the animals at the farm were goats? Levae your answer correct to 2 decimal places.

Solution

* 180 more hens than ducks, therefore hens --> 15% + 180.
** Ducks (15%) and hens (15% + 180), therefore goats give the remaining 70% less 180.

70% - 180 --> 121
70% --> 121 + 180 = 301
10% --> 301 divided by 7 = 43
100% 10 x 43 = 430

Percentage of animals were goats
--> (121/430) x 100% = 28.139% ~ 28.14%

Answer: 28.14%

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CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q10

In September, Rafael received a monthly salary of $2698 and she saved 20% of it. In December, her salary was reduced by 5% and she continued to save 20% of her salary. How much less was her savings in December compared to that in September? Leave your answer correct to the nearest dollar.

Solution

Sep --> 20% x $2698 = $539.60

5% x 539.6% = $26.98 ~ $27

Answer: $27

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CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q5

The number of visitors to the zoo has been increasing by 8% each year since the year 2003. If the number of visitors in 2003 was 12 500, how many visitors went to the zoo in 2005?

Solution

Yr 2003 --> 12 500
Yr 2004 --> 108% x 12 500 = 13 500
Yr 2005 --> 108% x 13 500 = 14 580

Answer: 14 580 visitors

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CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q4

A department store was offering a promotion for customers who bought T-shirts. Any customer who bought 3-T shirts would get a 50% discount on the 3rd T-shirt. Pamela bought 3 T-shirts and paid an average cost of $11.90 for each T-shirt. Find the orginal price of one T-shirt.

Solution

Original Price of 1 T-shirt --> 2 units
Price of 3rd T-shirt --> 1 unit

2 T-shirts at original price + 1 discounted price T-shirt --> $11.90 (avg)
(2 x 2 units) + 1 unit --> $11.90 x 3 = $37.50 (total)
4 units + 1 unit --> $37.50
5 units --> $37.50
1 unit --> $37.50 divided by 5 = $7.14
2 units --> 2 x $7.14 = $14.28

Answer: $14.28

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q18

Ai Tong School organized a 2-day camp. On the first day, the number of boys was 600 more than the girls. On the second day, the number of boys decreased by 10% but the number of girls increased by 10%. If there were 2540 children on the second day, how many children were there on the first day?

Solution

2nd Day

Boys --> 0.9 unit + 540

Girls --> 1.1 unit

Total --> 2540

0.9 unit + 540 + 1.1 unit --> 2540

2 units + 540 --> 2540

2 units --> 2540 - 540 = 2000

1 unit --> 2000 divided by 2 = 1000

1st Day

2 units + 600

(2 x 1000) + 600

= 2000 + 600

= 2600

Answer: 2600 children

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q17

75% of the children in the stadium were girls. After 52 girls and 4 boys left, the remaining children formed groups of 8. In each group, there were 3 boys. How many children were there in the stadium at first?

Solution

Note - "Before" for girls is 3 parts, while "Before" for boys is 1 part. This is to represent 75% girls and 25% boys, before 52 girls and 4 boys left.

From the table above

4 units --> 40

1 unit --> 40 divided by 4 = 10

Total boys (after)

3 units --> 3 x 10 = 30

Total girls (after)

5 units --> 5 x 10 = 50

Total children (after)

30 + 50 = 80

Total children at first

80 + 52 + 4 = 136

Answer: 136 children

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q11

James spends 20% of his monthly income on transport, 30% of it on food and 10% of the remainder on clothes. He saves the rest of his income. If his monthly savings is $900, find his monthly income.

Solution






(Saves)
90% of 50% --> $900
(90/100) x (50/100) x 100% --> $900
45% --> $900
1%--> $900 divided by 45 = $20

(Monthly Income)
100% --> 100 x $20 = $2000

Answer: $2000

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q7

The table below shows the rates for water consumption.

a) Find the amount paid for 50 cubic metres of water used.

b) If 7% GST is imposed on the total amount, how much is the GST correct to the nearest 10-cent?

Water Consumption Rates

First 20 cubic metres ----- $1.33 per cubic metre

Next 20 cubic metres ----- $1.46 per cubic metre

Additional amount above 40 cubic metres ----- $1.73 cubic meter

Solution

a)

1st 20 cubic metres --> 20 x $1.33 = $26.60

2nd 20 cubic metres --> 20 x $1.26 = $29.20

Next 10 cubic metres --> 10 x $1.73 = $17.30

Total Amount

--> $26.60 + $29.60 + $17.10 = $73.30

Answer: $73.10

b)

7 % x $73.10 = $5.117

Approximately --> $5.10 (to nearest 10-cent)

Answer: $5.10

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Rosyth Sch 2007 PSLE Math Prelim Q38

In the figure not drawn to scale, the ratio of the area of the bigger square to the smaller square is 8:4. If 25% of the larger square is shaded, what percentage of the whole figure is not shaded?


Solution



Portion unshaded ----- 6 units + 2 units = 8 units
Total area ----- 6 units + 2 units + 2 units = 10 units

Percentage of figure that is not shaded
8/10 x 100% = 80%

Answer: 80%