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