Mothers know best

Got this video clip from an ex-P6 student. She emailed it to us.

Mothers are designed all to be the same so that children will all grow up to be the same.

Rosyth Sch 2006 PSLE Math Prelim Q46

At a fun fair, there were 49 more children than women. There were 3/5 as many men as women. Given that the number of women was 25% of the total number of people at the fun fair, how many people were at the fun fair?

Solution

Men ----- 3 units
Women ----- 5 units
Children ----- 5 units + 49
Total ----- 13 units + 49

(Women) 5 units ----- 25%
1 unit ----- 25% divided by 5 = 5%
13 units ----- 13 x 5% = 65%

Remaining 49 people ----- 100% - 65% = 35%
35% ----- 49 people
(35% divided by 7)= 5% ----- (49 divided by 7) = 7
5% ----- 7
(5% x 20) = 100% ----- (7 x 20) = 140
100% ----- 7 x 20 = 140

Answer: There were 140 people at the fair.

Rosyth Sch 2006 PSLE Math Prelim Q45

Ali, Billy and Caven had some cards. Ali would have twice as many cards as Billy if Billy gave 28 cards to Ali. Both Billy and Caven would have the same number of cards if Caven gave 84 cards to Billy. Given that Caven had 112 more cards than Ali at the beginning, find the number of cards each of them had at the beginning.

Solution

Ali ----- 2 units – 28 (at first)
Billy ----- 1 unit + 28 (at first)
Caven ----- 1 unit + 28 + 84 + 84 (at first)

At first,
(Caven) – (Ali) ---- 112
(1 unit + 28 + 84 + 84) – (2 units – 28) ----- 112
(1 unit + 196) – (2 units – 28) ----- 112
224 – 1 unit ----- 112
224 – 112 ----- 1 unit
1 unit ---- 112

Ali at first
(2 x 112) – 28 = 196

Billy at first
(112) + 28 = 140

Caven at first
(112) + 28 + 84 + 84 = 308

Answer: Ali had 196, Billy had 140 and Caven had 308

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.