Raffles Girls Pri Sch 2007 PSLE Math Prelim Q43

There are some red and green beads in a container. If 75 more green beads are put into the container, the percentage of red beads will decrease from 30% to 20%. How many red beads are in the container?

Solution



12 units ----- 7 units + 75
5 units ----- 75
1 unit ----- 75 divided by 5 = 15

Red at first
3 units ----- 3 x 15 = 45

Answer: 45 red beads

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q41

Jane started driving at 9.30 am from Town A to Town B. At 11.30 am, Jane had covered only 2/5 of the distance. She had to cover another 144 km before she reached Town B.

(a) What was the distance between Town A and Town B?

(b) If Jane were to travel at an average speed of 72km/h after 11.30 am, at what time would she reach Town B?
(Express your answer using the 24-hour clock)

Solution


(a)
3 units ----- 144 km
1 unit ----- 144 km divided by 3 = 48 km
5 units ----- 5 x 48 km = 240 km

Answer: 240 km


(b)
Time = 144km divided by 72 km/h = 2 h
2 hours after 11.30 am is 1.30 pm or 1330 h.

Answer: 1330 h

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q40

A rectangular tank with 5 identical solid metal cubes was filled to the brim with water. Water was drained out of the tank through a tap at a rate of 2 litres per minute. It took 18 minutes for the water level to drop to the height of the metal cubes. Find the volume of the 5 metal cubes.



Solution

Volume of whole tank
60 cm x 20 cm x 40 cm = 48 000 cubic cm or 48 litres

1 min ----- 2 litres

18 min ----- 2 litres x 18 = 36 litres

Volume of tank filled with water + volume of cubes after 18 min
48 litres – 36 litres = 12 litres or 12 000 cm

Height of cubes is therefore,
Height ------ Volume divided by base area
= 12 000 cubic cm divided by (60 cm x 20 cm) = 10 cm

Height of cube ------ 10 cm
Volume of 1 cube ----- 10 cm x 10 cm x 10 cm = 1000 cubic cm
Volume of 5 cubes ----- 1000 cubic cm x 5 = 5000 cubic cm

Answer: 5000 cubic cm

Anglo Chinese School 2007 PSLE Math Prelim Q48

Mr Goh was travelling from Town X to Town Y. After completing 2/7 of the journey, he passed by Mr Lee travelling the same direction. Mr Lee was travelling at an average speed of 60 km/h. Mr Goh reached his destination 3 hours later, while Mr Lee was still 45 km away from Town Y.

(a)Find the distance between the two towns.
(b)If Mr Lee left Town x at 11.30 am, what time would he arrive at Town Y?

Solution



(a)
(Goh) 5/7 of journey ----- 225 km
1/7 of journey ----- 225 km 5 = 45 km
(Whole journey) 7/7 ----- 45 km x 7 = 315 km

Answer: 315 km


(b)
Lee’s time ----- distance divided by speed
315 km divided by 60 km/h
= 5.25 hours or 5 hours 15 min

Since Lee left at 11.30 am, he would arrive at 4.45 pm.

Answer: 4.45 pm

Anglo Chinese School 2007 PSLE Math Prelim Q47

In an auditorium, the ratio of the number of competitors to the number of non-competitors is 8:5. The ratio of the number of male competitors to the number of female competitors is 7:4. Given that 3/5 of the non-competitors are males and there are 32 female competitors, how many males and females are there in the auditorium?

Solution



Males ----- 56 + 33 = 89
Females ----- 32 + 22 = 54

Answer: 89 males, 54 females

Anglo Chinese School 2007 PSLE Math Prelim Q46

A rectangular container measuring 45 cm by 10 cm by 20 cm is empty at first. Water flows from Tap X at a rate of 1.3 litres per minute and from Tap Y at a rate of 1.2 litres per minute. How long does it take to completely fill up the container if both taps are turned on at the same time? Give your answer in minutes and seconds.

Solution



Volume of tank ----- 45 cm x 10 cm x 20 cm
= 9000 square cm or 9 litres

1 min ----- 1.3 litres/min + 1.2 litres/min = 2.5 litres/min

9 litres divided 2.5 litres/min = 3.6 min or 3 min 36 seconds


Answer: 3 min 36 seconds

Anglo Chinese School 2007 PSLE Math Prelim Q45

The figure is made up of three circles and two semi-circles. O is the center of the circle. AB is 42 cm. Find the total area of the shaded part.





Area of 1 square ----- (10.5 x 10.5)square cm = 110.25 square cm

Area of 2 squares ----- 2 x 110.5 square cm = 220.5 square cm

Area of shaded area is ---- Area of whole figure – area of 1 small circle – area of 4 small quadrants – area of 2 squares

(1386 - 346.5 - 346.5 - 220.5) square cm = 472.5 square cm

Answer: 472.5 square cm

Anglo Chinese School 2007 PSLE Math Prelim Q44

Marvin bought a box of fruits. 30% of the fruits are apples and the rest are oranges. He realized that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found that there were 52 more fruits in the box. How many fruits were there in the box at first?

Solution

At first
Apples ----- 30%
Oranges ----- 70%

Threw half apples away, bought 40% more oranges,
Apples ----- 1/2 x 30% = 15%
Oranges ----- 70% + (40/100 x 70%) = 98%

Total ----- 15% + 98% = 113%

113% - 100% = 13% (increase in number of fruits)
13% ----- 52 fruits
1 % ----- 52% divided by 13 = 4

Number of fruits at first,
100% ----- 4 x 100 = 400

Answer: 400 fruits

Anglo Chinese School 2007 PSLE Math Prelim Q43

Derrick had 2/3 as many stickers as Benedict. After Derrick bought another 8 stickers and Benedict lost 5 stickers, Derrick now has 4/5 as many stickers as Benedict. Find the number of stickers Derrick and Benedict had at first.

Solution



(Derrick after)
4 parts ----- 2 units + 8
2 parts ----- 1 unit + 4
2 parts ----- 1 part + 13 + 4
2 parts – 1 part ----- 17
1 part ----- 17

1 unit – 13 ----- 17
1 unit ----- 17 + 13 = 30
5 units ----- 30 x 5 = 150

Answer: 150 stickers

Anglo Chinese School 2007 PSLE Math Prelim Q41

Alex has $1.50 more money than Betty and three times as much money as Colin. The 3 of them have $9.70 altogether. How much does Colin have?

Solution



7 units - $1.50 ----- $9.70

7 units ----- $9.70 + $1.50 = $11.20

1 unit ----- $11.20 divided by 7 = $1.60


Answer: $1.60