Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q16

The number of pupils in Team A to the number of pupils in Team B is in the ratio of 7:6. If 45 pupils are transferred from Team A to Team B, the ratio will become 2:3. How many pupils are there altogether?

Solution

Note - "Before" is multiplied by 5, while "After" is multiplied by 13 so as to have an equal number of total units of 65 each. The total number of units for "Before" and "After" are the same because there was no increase or decrease in the total number of pupils before or after the transfer.

Team A had a decrease of

35 units – 26 units --> 45 (pupils)

9 units --> 45

1 unit --> 45 divided by 9 = 5

Total number of pupils

Team A + Team B

26 units + 39 units --> 65 units

65 units --> 5 x 65 = 325

Answer: 325 pupils

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q15

At a party, only 4/9 of the invited guests came. The ratio of the number of women to the number of men present was 3 : 4. If 80 more men turned up for the party, the number of men would be twice the number of women. How many guests were invited?

Solution

Before 80 more men turned up

Women : Men

3 : 4

After 80 more men turned up

Women : Men

3 : 6

There was an increase of 2 units for men

2 units --> 80 (men)

1 unit --> 80 divided by 2 = 40

Total present at the party before 80 more men turned up

7 units --> 280

4/9 of invited guests --> 280

1/9 --> 280 divided by 4 = 70

All invited guests

9/9 --> 9 x 70 = 630

Answer: 630 guests

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q14

For every 200 books Johnson sells, he earns $8. He will receive an addition of $20 for every 3000 books sold. How many books must he sell to earn $700?

Solution

1 group of 200 books --> $8

3000 books divided by 200 books --> 15 groups of 200 books

15 groups of 200 books

--> 15 x $8 + $20 commission

= $120 + $20

= $140

To earn $700,

$700 divided by $140 --> 5 groups of $140

1 group of $140

--> 15 groups of 200 books

5 groups of $140 --> 5 x 15 groups of 200 books

=75 groups of 200 books

75 groups of 200 books

--> 75 x 200 books

= 15 000 books

Answer: 15 000 books

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q13

The length of a rectangle is thrice as long as its width. Its perimeter is 16p cm.

a) Find the length of the rectangle in terms of p.

b) Find the area of the rectangle if p = 4.

Solution

Perimeter

--> 3 units + 1 unit + 3 units + 1 unit

= 8 units

8 units --> 16p cm

1 unit --> 16p cm divided 8 = 2p cm

a)

Length

3 units --> 3 x 2p cm = 6p cm

Answer: 6p cm

Answer: 192 square cm

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q12

20 similar pails of water can fill 5/12 of a container. Another 8 similar pails and 105 similar bowls of water are needed to fill the container to its brim. How many such bowls of water are needed to fill the empty container completely?

Solution

20 pails --> 5/12 of container (x2)

8 pails + 105 bowls --> remaining 7/12 of container (x5)

40 pails --> 10/12 of container (after x2)

40 pails + 525 bowls --> 35/12 containers (after (x5)

From the above we can see that 525 bowls can fill up:-

525 bowls --> 35/12 - 10/12 = 25/12 containers

25/12 --> 525 bowls

1/12 --> 525 divided 25 = 21 bowls

(Full container) 12/12 --> 12 x 21 = 252

Answer: 252 bowls

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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 Q10

The diagrams below show tiling patterns. Each tile is a square of side 1 cm.

What is the perimeter of Pattern 10?

Solution

(Add 6 cm for every new pattern)

Pattern 1 --> 10 cm

Pattern 2 --> 16 cm

Pattern 3 --> 22 cm

Pattern 4 --> 28 cm

Pattern 5 --> 34 cm

Pattern 6 --> 40 cm

Pattern 7 --> 46 cm

Pattern 8 --> 52 cm

Pattern 9 --> 58 cm

Pattern 10 --> 64 cm

Answer: 64 cm

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q9

A snail fell into a well that is 300 cm deep.

In the first hour, it climbed 80 cm up the well.

In the second hour, it climbed 70 cm up the well.

Each hour, it managed to climb 10 cm less than the hour before.

How many hours did it take to climb out of the well?

Solution

1st h --> 80 cm

2nd h --> 70 cm

3rd h --> 60 cm

4th h --> 50 cm

5th h --> 40 cm

(80 + 70 + 60 + 50 + 40) cm = 300 cm

--> 5 hours

Answer: 5 h

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q8

The rectangle ACEG is divided into 4 parts. BCEF is a square. Each part has a different area. Find the area X.

Area of X

--> 4 cm x 3 cm = 12 square cm

Answer: 12 square cm

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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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