Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q18

The figure below shows 2 completely-filled tanks being emptied of the water from 2 different taps.

The taps at Tank A and Tank B were turned on at 7 am and 8.30 am respectively, until both tanks were completely empty. At 11 am, the water level in both the tanks was the same. At 12.30 pm, Tank B was completely empty and Tank A was only completely empty at 1 pm. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank A?

Solution

** At 11 am, water level in both Tanks were the same.

Note that 3/8 of B's height is the same as 2/6 or 1/3 of A's height.

(3/8) of B ----- (2/6) or (1/3) of A

(1/8) of B ----- (1/3) of A divided 3 = (1/9) of A

(8/8) of B (B's height) ----- 8 x (1/9) = (8/9) of A

* Remaining (1/9) of A ----- 5 cm
(This is the difference in height between Tank A and B)


(9/9) of A (A's height) ----- 9 x 5cm = 45 cm

Answer: 45 cm

Printer Friendly Version

RGS Primary 2009 PSLE Math Prelim Paper 2 Q12

Tap A, Tap B, Tap C and an empty rectangle tank are shown below.

Lily turned on Tap A with water flowing at a rate of 5 litres per minute. After 2 minutes, she placed a rock of volume 1250 cubic cm in the tank and turned on Tap B and Tap C as well. Tap C drains the tank at the rate of 2 litres per minute. After 5 more minutes, Lily turned off all the taps and noted that the height of the water level was 30 cm. Find the rate of the flow of water from Tap B.

Solution

Tap A (water filled into tank)

--> 5 litres x 7 (min) = 35 litres

Tap B (water drained from tank)

-->2 litres x 5 (min) = 10 litres

Volume of water in tank in the end

--> (50 x 30 x 30) cubic cm - 1250* cubic cm

= (45 000 - 1250) cubic cm

= 43 750 cubic cm

* volume of stone

43 750 cubic cm is the total volume of water filled through Tap A and Tap B less the volume of water drained from Tap C.
Tap A + Tap B - Tap C --> 43 750 ml

Tap B --> 43 750 ml - Tap A + Tap C
= 43 750 ml - 35 000 ml + 10 000 ml

= 18 750 ml (after 5 min)

1 min --> 18 750 ml divided by 5

= 3750 ml/min

= 3.75 litres/min

Answer: 3.75 litres/min

Printer Friendly Version

ACS Primary 2009 PSLE Math Prelim Paper 2 Q12

Water flows from Tap A at a rate of 250 ml per minute and from Tap B at a rate of 350 ml per minute. When both taps are turned on for 9 minutes, the water from both taps fill a container with a square base of side 25 cm. What is the height of the water level?

Solution

Tap A
1 min --> 250 ml
9 min --> 9 x 250 ml = 2250 ml

Tap B
1 min --> 350 ml
9 min --> 9 x 350 ml - 3150 ml

Total --> 2250 ml + 3150 ml = 5400 ml


Volume of cuboid = Base area x height
5400 cubic cm = 25 cm x 25 cm x height
5400 cubic cm = 625 square cm x height
height = 5400 cubic cm divided by 625 square cm
height = 8.64 cm

Answer: 8.64 cm

Printer Friendly Version

ACS Primary 2009 PSLE Math Prelim Paper 2 Q7

A bar of chocolate is sold at $3.50 each or in packets of 4 at $12 per packet. Alice wants to buy exactly 38 bars of chocolate for a party. What is the least amount of money that Alice could have spent on the chocolates?

Solution

38 bars --> 36 bars + 2 bars
--> 9 packets of 4 bars + 2 individual bars
--> (9 x $12) + (2 x $3.50)
= $108 + $7
= $115

Answer: $115

Printer Friendly Version

ACS Primary 2009 PSLE Math Prelim Paper 2 Q5

If it takes 1 worker 4 days to paint a flat, how many days will it take 8 workers to paint 4 flats if they all work at the same rate?

Solution

1 worker --> 1 flat, 4 days

8 workers --> 8 flats, 4 days
(8 workers give an output 8 times more)

8 workers --> 4 flats, 2 days
(Same 8 workers need only half the time for 4 flats)

Answer: 2 days

Printer Friendly Version

CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q13

Abbie, Ellen and Faheem sold umbrellas to raise funds for charity. Each umberlla was priced at $22.50. Abbie sold 1/6 of the umbrellas while Ellen and Faheem sold the remaining umbrellas in the ratio of 2:7 respectively. If Faheem sold 364 umbrellas more than Abbie, what was the total amount of money collected by them?

Solution

Abbie --> 1/6
Remaining --> 5/6

Since ratio for Ellen : Faheem is 2 : 7,
Faheem sold 7/9 of remainder

Faheem (7/9 of the remaning 5/6)
--> 7/9 x 5/6 = 35/54

(Faheem - Abbie) --> 35/54 - 1/6 = 13/27
13/27 --> 364 (Faheem sold 364 more than Abbie)
1/27 --> 364 divided by 13 = 28
27/27 --> 27 x 28 = 756

756 x $22.50 = $17 010

Answer: $17 010

Printer Friendly Version

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

Printer Friendly Version

Rosyth Sch 2007 PSLE Math Prelim Q41

The table below shows the rates at which a construction worker is being paid daily.

How many hours must he work in a day to earn $140?

Solution

First 8 hours of work ----- $10 x 8 = $80

To earn $140, he needs another $60.

Overtime rate is ----- $10 per hour x 1.5 = $15 per hour.

For overtime pay to be equal to $60, he must work
$60 divided by $15 per hour = 4 hours

Total time he needs to work
8h + 4h = 12h

Answer: 12 hours

Rosyth Sch 2007 PSLE Math Prelim Q40

Machine A can do a printing job in 2 hours. Machine B can do the same job in 3 hours. If both machines are used at the same time, how long would it take to complete half the printing job?

Solution

Since Machine A takes 2 hours and Machine B takes 3 hours, Machine A will be able to get more work done than Machine B, if both are used at the same time, in the ratio of 3:2 as shown below.



(Machine A)
Whole job ----- 2 hours
3/5 of job ----- 3/5 x 2 hours = 6/5 hours

Time taken if both machines are used at the same time is 6/5 hours because while Machine A completes 3/5 of the job, Machine B completes the remaining 2/5 of the job.

Time taken for whole job done if both machines are used at same time is therefore 6/5 hours

Time taken for half the job done if both machines are used at the same time is
1/2 x 6/5 hours = 3/5 hour.

Answer: 3/5 hour

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 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

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 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.

Nanyang Pri Sch P6 CA1 2008 Math Q38

Two identical taps, when turned on at the same time, take 5 minutes to release 10 litres of water. How many such taps, when turned on at the same time, are needed to release 27 litres of water in 3 minutes?

Solution

2 taps, 5 min ----- 10 litres
2 taps, 1 min ----- 10 litres divided by 5 = 2 litres
1 tap, 1 min ----- 2 litres divided by 2 = 1 litre

27 litres, 1 min ----- 27 litres x 1 = 27 litres

27 litres, 3 min (3x slower than 1 min)
----- 27 divided by 3 = 9

Answer: It took 9 taps

Tao Nan School P5 SA2 2007 Math Q46

The table below shows the rates of charges for water consumption.

First 5 cubic metres ----- $1.50 per cubic metre
Next 5 cubic metres ----- $1.75 per cubic metre
Every additional 1 cubic metre or part thereof ---- $2.00 per cubic metre

a) In the month of June, Family A used 18 cubic metres of water. How much did Family A pay for their water bill?

b) Family A’s water bill for July was $48.25. How much water was used?

Solution

a)
Charges for 18 cubic metres -----

First 5 cubic metres ----- $1.50 x 5 = $7.50
Second 5 cubic metres ----- $1.75 x 5 = $8.75
Last 8 cubic metres ----- $2 x 8 = $16.00

Total charges ----- $7.50 + $8.75 + $16 = $32.25

Answer: The family paid $32.25


b)
First 10 cubic metres cost ----- $7.50 + $8.75 = $16.25

48.25 - $16.25 = $32

$32 was charged at a rate of $2 per metre cube -----
$32 divided by $2 per metre cube = 16 cubic metres

Total consumption ----- 10 + 16 = 26

Answer: 26 cubic metres of water was used.

Tao Nan School P5 SA2 2007 Math Q42

A rectangular fish tank 80 cm long and 60 cm wide is filled with water from a tap which flows at a rate of 3 litres per minute. If the tap is turned off after 40 minutes, what is the height of the water level in the container?

Solution

1 minute ----- 3 litres or 3000 ml
40 minutes ----- 40 x 3000 ml
= 120 000 ml or 120 000 cubic cm

Height of water level -----

Volume = length x base x height
120 000 cubic cm = 80 cm x 60 cm x height
120 000 cubic cm = 4800 square cm x height
Height = 120 000 cubic cm divided by 4800 square cm
Height = 25 cm (Answer)

Tao Nan School P5 SA2 2007 Math Q36

A baking machine can bake 20 muffins in 10 minutes. At this rate, how long does this machine take to bake 48 muffins?

Solution

Unit Method
20 muffins ----- 10 min
1 muffin ----- 10 min divided 20 = ½ min
48 muffins ----- ½ min x 48 = 24 minutes


Ratio Method
Muffins : Minutes
20 : 10
2 : 1
48 : 24

Answer: It takes 24 minutes to bake 48 muffins

Catholic High Sch 2006 PSLE Math Prelim Q42

It takes Martin 5 hours to fix a jigsaw. If Jeremy helps him, they would take 3 hours to fix the jigsaw together. How long will Jeremy take to fix the jigsaw by himself?

Solution

Martin
5h ----- 1 whole
3h ----- 3/5

Jeremy fixed the other 2/5
2/5 ----- 3h
1/5 ----- 3h/2
5/5 ----- (3h/2) x 5 = 7.5h

Answer: It will take Jeremy 7.5h

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.

Maha Bodhi Sch 2007 PSLE Math Prelim Q48

Two different machines, A and B, were used together at the same time to print a book. It took two hours for the book to be printed. If only Machine A was used, it would have taken another 4 hours. How long would it take to print the same book if only Machine B was used?

Solution

Machine A only ----- 2 hours + 4 hours = 6 hours

6 hours ----- Machine A printed whole book
2 hours ----- Machine A printed 1/3 book

The other 2/3 of the book was printed by Machine B
2 hours ----- Machine B printed 2/3 book
2/3 book ----- 2 hours
3/3 book ----- 3 hours

Answer: It would take 3 hours if Machine B was used only.