Pei Chun Public Sch 2007 PSLE Math Prelim Q48

Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.

Solution

(Note: The working has been amended (in blue) on 17 Sep 08 to make the working clearer.)

Cost of 1 dictionary ----- 1 unit + $4
Cost of 1 comic ----- 1 unit

Comics ----- 120%
Dictionary ----- 100%
Total 220% ----- $1496

10% ----- $1496 divided by 22 = $68
(Dictionaries) 100% ----- $680 

Comics ----- $1496 - $680 = $816

But we know that the ratio

comics : dictionaries

3 : 2

Comics

3 units ----- $816

1 unit ----- $272

Dictionaries

2 units + ? groups of $4 ------ $680

(2 x $272) + ? grps of $4 ----- $680

? grps of $4 ----- $680 - $544 = $136

? grps ----- $136 divided by 4 = 34 groups of $4

[Every $4 difference ---- 1 dictionary was bought

$136 difference ----- $136 divided by $4 = 34 (dictionaries)]

Dictionaries ----- $680
$680 divided by 34 dictionaries = $20 per dictionary

Answer: One dictionary cost $20.

Pei Chun Public Sch 2007 PSLE Math Prelim Q47

Najip, Kumar and Gurmit started jogging at the same time from the same starting-point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout.
a) What was the ratio of Gurmit’s speed to Najip’s speed to Kumar’s speed?

b) When Gurmit and Najip met again at the starting-point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track?



b)
(Gurmit)
5 min ----- 1 round
15 min ----- 3 rounds

Kumar (since ratio Gurmit : Kumar is 2:3) ----- 4.5 rounds
3.6 km divided by 4.5 rounds = 0.8 km per round

Answer: The circumference is 0.8 km

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Update - 1420 hours, 29 Aug 2008

I have relabelled the model to make it clearer.
The model is seen from Gurmit’s perspective.
He was running in the opposite direction as compared to the other two.

In the 5 min cycle, Gurmit will see Kumar after 2 min.
This means G would have covered 2/5 of lap when he met K.
It also means K would have covered 3/5 lap at that point.
Hence, the model shows 2 units for G and 3 for K.

In the same 5 min cycle, G will meet N after 3 min.
This means G would have covered 3/5 lap when he met N.
Of course, N would have covered 2/5 lap.
Hence, 3 units for G and 2 for N.

Pei Chun Public Sch 2007 PSLE Math Prelim Q46

A rectangular tank measuring 60 cm by 40 cm and 20 cm was 1/6 filled with water. At 08 00, Tap A with water flowing out at a rate of 3 litres per minute was turned on. At 08 02, Tap B was turned on to drain water out of the container at a fixed rate. At 08 13, the tank was 75% filled with water. At what time would the tank be filled to the brim?



Solution

Capacity of tank -----
(60 cm x 40 cm x 20 cm) = 48 000 cubic cm or 48 000 ml

1/6 of volume ----- 48 000 ml x 1/6 = 8000 ml

Water flowed for 2 min ----- 3 litres x 2 = 6000 ml

Amount of water in tank at 08 02 -----
8000 ml + 6000 ml = 14000 ml

75% volume ----- 48 000 ml x 75% = 36 000 ml

From 08 02 to 08 13 ----- 11 min

Rate of increase of water level in tank -----
(36 000 – 14 000) ml divided by 11 min
= 2000 ml per min

To be filled to the brim from 75% volume, another 25% volume must be filled.

25% volume ---- 48 000 ml x 25% = 1200 ml
Time needed ----- 12 000 ml divided by 2000 ml per min = 6 min

6 min after 08 13 is 08 19

Answer: It would be 08 19 when the tank is filled to the brim.

Pei Chun Public Sch 2007 PSLE Math Prelim Q45

400 people took part in a camp. 73 of them were adults and the rest were children. 2/5 of the boys and ¼ of the girls were lower primary pupils while the rest of them were upper primary pupils. There were 9 more upper primary girls than upper primary boys.
a) How many upper primary pupils were there?
b) What percentage of the people who took part in the camp were girls?

Solution

400 people – 73 adults ----- 327 children



12 parts + 15 parts ----- 981 + 45
27 parts ----- 1026
1 part ----- 1026 divided by 27 = 38

a)
(Upp Pri Girls) 3 parts ---- 3 x 38 = 114
(Upp Pri Boys) 114 – 9 = 105
Total Upper Pri ----- 114 + 105 = 219
Answer: There were 219 upper primary pupils.

b)
(Total Girls) 4 parts ----- 38 x 4 = 152
Percentage of girls ----- (152/400) x 100% = 38%
Answer: 38% were girls.

Pei Chun Public Sch 2007 PSLE Math Prelim Q44

The figure below is made up of a rectangle, a semi-circle and 4 identical quadrants.
a) What is the total area of the shaded parts?
b) What is the perimeter of the whole figure?


Solution

a) Redrawing


Area of shaded area
= Area of rectangle + Area of quadrant
= (7 cm x 3.5 cm) + (¼ x 22/7 x 3.5 cm 3.5 cm)
= (24.5 + 9.625) square cm
= 34.125 square cm (Answer)

b)
Perimeter -----
Lengths of 4 quarter arcs + 6r
= 4 x (¼ x 2 x 22/7 x 3.5 cm) + (6 x 3.5) cm
= 22 cm + 21 cm
= 43 cm (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q43

Taufik arranged a rectangle and a square and painted them in three colours as shown in the figure below. The ratio of the area of the rectangle to that of the square is 3:1. The ratio of the area of the red part to that of the blue part is 4:1. The length of the square is 9 cm.
a) What is the area of the purple part?
b) What is the ratio of the area of the purple part to that of the figure?






Area of Rectangle : Area of Square
3 : 1
9 units : 3 units

Red Area : Blue Area
4 : 1
8 units : 2 units

a)
(Square) 3 units ----- 81 square cm
(Purple) 1 unit ----- 81 square cm divided by 3 = 27 square cm (Answer)

b)
Purple ----- 1 unit
Whole figure 11 units

Area of purple part : Area of whole figure
1 : 11 (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q42

The figure below shows a park which is made up of a triangular fitness area, a rectangular pond and a field in the shape of a trapezium. The length of the pond is twice its breadth.



a) The cost of fencing material is $3 per meter. How much will it cost to fence up the pond?
b) What is the area of the park?

Solution

a)
Length of pond ----- 2 x 4 m = 8 m
Perimeter of pond ----- 2 x (8 + 4) m = 24 m

1 m ----- $3
24 m ----- $3 x 24 = $72

Answer: It will cost $72 to fence up the pond.

b)
Area of rectangle -----
21 m x 4 m = 84 square m

Area of triangle -----
½ x 14 m x 21 m = 147 square m

Total area of the park ----- (84 + 147) square m = 231 square meters (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q41

The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers was 1 : 5. Then their mother gave Eunice 12 more stickers and Andrew 5 more stickers. The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers became 1 : 4. How many stickers did Andrew have in the end?

Solution

Andrew (before) 1 unit + 5 ----- 1 part (after) (multiply by 4)
Eunice (before) 5 units +12 ----- 4 parts (after)

Andrew (before) 4 units + 20 ----- 4 parts (after)
Eunice (before) 5 units + 12 ----- 4 parts (after)

Comparing Eunice with Andrew -----
(Eunice) 5 units + 12 ----- 4 units + 20 (Andrew)

5 units – 4 units ----- 20 – 12
1 unit = 8

Andrew in the end -----
1 unit + 5
= 8 + 5
= 13

Answer: Andrew had 13 stickers in the end.

Pei Chun Public Sch 2007 PSLE Math Prelim Q40

Kavita had 50% fewer erasers than Mark. After Mark gave 15 of his erasers to Kavita, Kavita had 40% fewer erasers than Mark. How many erasers did Kavita have at first?

Solution



Kativa has 30 more, while Mark has 15 less. Hence, Kativa will have 45 more than Mark.

45 ----- 120% - 100%
45 ----- 20%
10% ----- 45% divided by 2 = 22.5%

Kativa at first ----- 60% -15
= (6 x 22.5) - 15
= 135 – 15
= 120

Answer: Kativa had 120 erasers at first.

Pei Chun Public Sch 2007 PSLE Math Prelim Q38

A rectangular piece of cardboard measures 17 cm by 12 cm. Sushila cuts the greatest number of rectangular pieces, each measuring 3 cm by 2 cm, from the cardboard. What is the total area of all the pieces cut?

Solution
The diagram below is not drawn to scale



34 pieces of small rectangles can be cut without any cardboard left.

Area used ----- 17 cm x 12 cm = 204 square cm (Answer)