Rosyth Sch 2006 PSLE Math Prelim Q44

A rectangular tank 2.5 m long and 1.2 m wide is filled with water from two taps. Tap A fills it with water at the rate of 12 litres per minute and Tap B fills it up with water at the rate of 15 litres per minute. Both taps are turned on at the same time. What is the height of the water in the tank after 8 minutes?

Solution

Tap A ----- 12 litres per min
Tap B ----- 15 litres per min
Total ----- 27 litres per min

1 min ----- 27 litres
8 min ----- 8 x 27 litres = 216 litres or 216 000 cubic cm

Volume = Length x breadth x height
216 000 cubic cm = 250 cm x 120 cm x height
height = 216 000 cubic cm divided by (250 x 120) square cm

height = 7.2 cm (Answer)

Rosyth Sch 2006 PSLE Math Prelim Q43

Mrs Yu paid $16.20 for some eraser and pencils. An eraser cost 15 cents and a pencil cost 45 cents. She bought 12 more pencils than erasers. How many erasers did she buy?

Solution

1 eraser ----- $0.15
1 pencil ----- $0.45
1 set (of 1 eraser, 1 pencil) ----- $0.60

She bought -----
Unknown number of sets + 12 pencils ----- $16.20
(? x $0.60) + (12 x $0.45) ----- $16.20
(? x $0.60) + $5.40 ----- $16.20
? x $0.60 ----- $16.20 - $5.40 = $10.80
? ----- $10.80 divided by $0.60 = 18 (sets)

18 sets ----- 18 erasers

Answer: She bought 18 erasers.

Rosyth Sch 2006 PSLE Math Prelim Q42

The average mass of Bob and his five friends is 43 kg. Bob is 3 kg heavier than the average mass of his five friends. Find the mass of Bob.

Solution

Total mass of Bob and 5 friends -----
43 kg x 6 = 258 kg

If Bob had been 3 kg less, the total mass would be -----
258 kg – 3 kg = 255 kg

Average ---- 255 kg divided by 6 = 42.5 kg

But since Bob is 3 kg heavier -----
42.5 kg + 3 kg = 45.5 kg

Answer: The mass of Bob is 45.5 kg.

Rosyth Sch 2006 PSLE Math Prelim Q41

In the figure below, AB is parallel to DE and ACDG is parallel to EF. ABC is an isosceles triangle with Angle ABC = 36 degrees. Find Angle DEF.



Solution

Angle BAC ---- (180 – 36) degrees divided 2 = 72 degrees
Angle EDG ----- 72 degrees
Angle DEF ----- (180 – 72) degrees = 108 degrees (Answer)

Rosyth Sch 2006 PSLE Math Prelim Q40

The ratio of the number of girls to the number of boys in school A was 4:7. The ratio of the number of girls to the number of boys in school B was 3:8. The total number of pupils in school A was twice the total number of pupils in school B. Find the ratio of the number of boys in school A to the number of boys in school B. (Express your answer in its simplest form).

Solution

School A
Girls : Boys
4 : 7
(11 units total)

School B
Girls : Boys
3 : 8
(11 units total)

Since school A has twice the number of pupils as school B -----

School A
Girls : Boys
4 : 7
(11 units total)

Multiply by 2

School A
Girls : Boys
8 : 14
(22 units total)


Boys
School A : School B
14 : 8
7 : 4

Answer: The ratio is 7 : 4.

Rosyth Sch 2006 PSLE Math Prelim Q39

Paul would like the send a parcel to his friend in ABC country. The freight change is $8.00 per kg per km. What is the total charge for sending the parcel weighing 12 kg for 35 km?

Solution

1 kg ----- $8
12 kg ----- 12 x $8 = $96

1 km, 12 kg ----- $96
35 km, 12 kg ----- 35 x $96 = $3360

Answer: The total charge is $3360.

Rosyth Sch 2006 PSLE Math Prelim Q38

The pie chart shows the different kinds of fruits sold by Uncle Lim. He sold 425 mangoes. How many durians did he sell?



Solution

Durians ----- (100 – 25 – 12 – 15)% = 48%
(Mangoes) 25% ----- 425
1% ----- 425 divided by 25 = 17

Durians) 48% ----- 17 x 48 = 816

Answer: He sold 816 durians.

Rosyth Sch 2006 PSLE Math Prelim Q37

The figure below consists of two overlapping shapes, a square and a triangle. The ratio of the area of the square to the area of the triangle is 2 : 3. 1/8 of the square is shaded. The shaded area in the figure is 15 square cm. Find the area of the unshaded part of the figure.



Solution

Area of square
1/8 area ----- 15 square cm
8/8 area ----- 15 square cm x 8 = 120 square cm

Area of square : Area of triangle
2 : 3

(Square) 2 units ----- 120 square cm
1 unit ----- 120 square cm divided by 2 = 60 square cm
(Triangle) 3 units ----- 3 x 60 square cm = 180 square cm

Unshaded area ----- (Total area of square + total area of triangle - shaded area of the triangle - shaded area square)

(120 + 180 – 15 –15) square cm
= 270 square cm (Answer)

Rosyth Sch 2006 PSLE Math Prelim Q36

¼ of Edmund’s savings is the same as 1/6 of Rob’s savings. The difference in their savings is 1/5 of Kenny’s savings. Given that the total savings of the 3 boys is $340, how much money does Rob save?

Solution


20 units ----- $340
1 unit ----- $340 divided by 20 = $17
(Rob) 6 units ----- $17 x 6 = $102

Answer: Rob saves $102.

Rosyth Sch 2006 PSLE Math Prelim Q35

Daniel is thinking of three consecutive odd numbers. The average of the first and second number is 40, while the average of the second and third numbers is 42. List the three numbers.

Solution

Average of 1st and 2nd numbers ----- 40
Total of 1st and 2nd numbers ----- 40 x 2 = 80

Average of 2nd and 3rd ----- 42
Total of 2nd and 3rd ----- 42 x 2 = 84

Total of 1st and 3rd -----
(80 + 84) divided by 2 = 82

Average of 1st and 3rd -----
82 divided by 2 = 41

41 is also the middle number.
1st and 3rd numbers ----- 39 and 43

Answer: 39, 41, 43

Rosyth Sch 2006 PSLE Math Prelim Q34

For every 10 tickets purchased, a 20% discount will be given to the 10th ticket. If each ticket cost $8.50, how much did Keith have to pay for 12 tickets?

Solution

1 ticket ----- $8.50
9 tickets ----- 9 x $8.50 = $76.50
10th ticket ----- 80% x $8.50 = $6.80

10 tickets ----- $76.50 + $6.80 = $83.30
2 tickets ----- 2 x $8.50 = $17

Total for 12 tickets ----- $83.30 + $17 = $100.30

Answer: Keith had to pay $100.30

Rosyth Sch 2006 PSLE Math Prelim Q33

The graph below shows the distance traveled by Mark in 4 hours. What was Mark’s average speed?


Solution

Speed = Distance divided by time
Speed = 260 km divided by 4 h = 65 km/h (Answer)

Rosyth Sch 2006 PSLE Math Prelim Q32

Raj, Siva and Paul had $700 altogether. Raj spent 1/3 of his money, Siva spent $52 and Paul spent twice the amount of what Raj spent. The three of them had the same amount of money left. How much did Raj have at first?

Solution



9 units + $52 ----- $700
9 units ----- $700 - $52 = $648
1 unit ----- $648 divided by 9 = $72
(Raj) 3 units ----- 3 x $72 = $216

Answer: Raj had $216 at first.

Rosyth Sch 2006 PSLE Math Prelim Q31

Tammy has 24 fifty-cent coins. If she were to arrange all the coins to form the outline of a rhombus, what would be the total value of the coins on one side of the rhombus?

Solution

24 coins - 4 corners ----- 20 coins
20 coins divided by 4 sides ----- 5 coins per side

5 coins per side + 2 coins at the two corners ----- 7 coins
7 coins x $0.50 ----- $3.50

Answer: The value of the coins on one side will be $3.50

Rosyth Sch 2006 PSLE Math Prelim Q30

Mr Jamil bought a plasma TV set for which he had to pay a deposit of 35% of the selling price. How much was the deposit if the rest of the payment for the plasma TV set was $1625?

Solution

65% ----- $1625
1% ----- $1625 divided by 65 = $25
35% ----- 35 x $25 = $875

Answer: The deposit was $875.

Rosyth Sch 2006 PSLE Math Prelim Q28

A shopkeeper bought 52 eggs. She threw away 7 rotten eggs and sold the rest at $0.80 for 5 eggs. How much money did she collect in all after selling the eggs?

Solution

52 – 7 = 45 (eggs sold)
45 eggs divided by 5 eggs ----- 9 sets of 5 eggs
1 set ----- $0.80
9 sets ----- 9 x $0.80 = $7.20

Answer: She collected $7.20.

Rosyth Sch 2006 PSLE Math Prelim Q27

A number of coloured balls are in a basket. There are 145 more red balls than white balls. There are 358 more white balls than black balls. How many more red balls than black balls are there?

Solution

Red ----- 1 unit + 358 + 145
White ----- 1 unit + 358
Black ----- 1 unit

Red more than black ----- 358 + 145 = 503

Answer: There are 503 more red than black balls.

Rosyth Sch 2006 PSLE Math Prelim Q26

The average mass of 4 girls, Gale, Nancy, Rani and Fiona is 4p. Gale weighs 2p kg, Nancy weighs p kg and Rani weighs 56 kg. What is the mass of Fiona?

Solution

Total of 4 girls ----- 4p kg x 4 = 16p kg

Fiona ----- (16p – 2p – p – 56) kg
= (13p – 56) kg (Answer)