Q&A - PSLE Math

[fightingmom]

Hi,


Please help with the following 2 questions:

(1) 450 people took part in a race. 97 of them were children and the rest were adults. 3/5 of the women and 3/4 of the men were married while the rest of them were singles. There were 15 more married men than married women.

(a) How many singles were there ?
(b) what fraction of the people who took part in the race were men ?



(2) in 2007, there were 90 more girls than boys in ABC school. In 2008, there were 1/3 fewer girls and the number of bigs increased by 5/9, resulting in a total of 660 pupils.

(a) what fraction of the pupils in 2007 were boys?
Express your answer in its simplest form

(b) in 2009, the number of girls increased while the number of boys remained the same in 2008. The ratio of the number of girls to the number of boys in 2009 was the same as the ratio in 2007.
How many pupils were there in 2009?


TIA !

[tianzhu]

fightingmom:

Hi,


Please help with the following 2 questions:

(1) 450 people took part in a race. 97 of them were children and the rest were adults. 3/5 of the women and 3/4 of the men were married while the rest of them were singles. There were 15 more married men than married women.

(a) How many singles were there ?
(b) what fraction of the people who took part in the race were men ?

Hi

This question has been discussed before.

A neat way is to use MD.Replace the W amd M with boxes of different sizes.

450-97 ----- 353
3M-3W ------15
M is 5 more than W

4W + 20 + 5W ------353
1W ------- 37
1M -------42

a)Singles --------- (37*2)+42 ------116
b)Men -------42*4 ------168
168/450 ------ 28/75

Best wishes

[tianzhu]

fightingmom:

(2) in 2007, there were 90 more girls than boys in ABC school. In 2008, there were 1/3 fewer girls and the number of bigs increased by 5/9, resulting in a total of 660 pupils.

(a) what fraction of the pupils in 2007 were boys?
Express your answer in its simplest form

(b) in 2009, the number of girls increased while the number of boys remained the same in 2008. The ratio of the number of girls to the number of boys in 2009 was the same as the ratio in 2007.
How many pupils were there in 2009?

Hi

This question has been discussed before.

You may wish to draw a MD.

2007
Girls ------9units+90
Boys ------9units

2008
Girls ------6units+60
Boys ------14units (increased by 5/9)

20 units +60 ------660
1 unit -------30

a)In 2007, boys --------9*30 -----270 and girls --------360
Therefore 270/630 --------3/7

In 2008, boys ------ 14*30 ------ 420

In 2007 Girls: Boys ------- 360:270 ------4:3

In 2009 Boys ------420, Girls -----560

Therefore total number ------- (420+560) -------980

Best wishes

[fightingmom]

:thankyou: , tianzhu !

[elkniwt]

Dear tianzhu,


Thank you very much!!! Thank you!!

Regards.

tianzhu:

elkniwt:

Hello,

Need help in this qn from Henry Park 2011 Prelim :

http://i48.tinypic.com/2i7qozm.jpg\">

Thanks!!

Hi

Please refer to earlier discussion.

Best wishes

http://www.kiasuparents.com/kiasu/forum/viewtopic.php&f=69&t=280&p=778481

But I think, there are added shaded portions inside the image as this is the duplicated set.

I’d go for

½ of square (12*12) – ½ of semicircle (r6) ------- 15.45

Area of 1 quadrant (r6) -------- 28.27

Total area ------ 43.72 (15.45 + 28.27)

Best wishes

[Winx5015]

Q1). At 6 am, a car left Town A for Town B at a speed of 65km/h. At the same time, another car left Town B for Town A at a speed of 55km/h. The distance between the two towns was 720km. At what time did the 2 vehicles pass each other?


Q2). A shopkeeper had some markers in red and blue. If 50 red markers and 25 blue markers were sold each week, there would be 500 red markers left when all the blue markers were sold. If 25 red markers and 50 blue markers were sold each week, there would be 800 red markers left when all the blue markers were sold. How many markers did the shopkeeper have at first?

Q3). A rectangular tank measuring 40cm by 30cm by 40cm was 1/6 filled with water. At 0930h, Tap X with water flowing out at a rate of 3 litre per minute was turned on. At 0932h, Tap Y was turned on to drained water out of the tank at a fixed rate. At 0943h, the tank was 75% filled with water. At what time would the tank be filled to the brim?

Thanks

[MathIzzzFun]

Winx5015:

Q1). At 6 am, a car left Town A for Town B at a speed of 65km/h. At the same time, another car left Town B for Town A at a speed of 55km/h. The distance between the two towns was 720km. At what time did the 2 vehicles pass each other?


Thanks

Hi

Time taken to meet = 720 / (55+65) h = 6h
6am + 6h --> 12.00pm
They will meet at 12.00pm


http://tinyurl.com/mathizzzfun-speed-notes01

cheers.

[MathIzzzFun]

Winx5015:

Q2). A shopkeeper had some markers in red and blue. If 50 red markers and 25 blue markers were sold each week, there would be 500 red markers left when all the blue markers were sold. If 25 red markers and 50 blue markers were sold each week, there would be 800 red markers left when all the blue markers were sold. How many markers did the shopkeeper have at first?

Thanks

Hi

Case 1:
Markers sold, Red : Blue --> 50 : 25 = 2 : 1 --> 4u : 2u (*using 2u for Blue because all the blue markers were sold in both cases)
Total number of red markers --> 4u + 500
Total number of markers --> 6u + 500
Case 2:
Markers sold, Red : Blue --> 25 : 50 = 1 : 2 --> 1u : 2u
Total number of red markers --> 1u + 800

Number of red markers are the same in both cases:
4u + 500 = 1u + 800
1u --> 100
Total number of markers --> 6 x 100 + 500= 1100

cheers.

[tianzhu]

Winx5015:

Q1)

Q3). A rectangular tank measuring 40cm by 30cm by 40cm was 1/6 filled with water. At 0930h, Tap X with water flowing out at a rate of 3 litre per minute was turned on. At 0932h, Tap Y was turned on to drained water out of the tank at a fixed rate. At 0943h, the tank was 75% filled with water. At what time would the tank be filled to the brim?

Thanks

Hi

Good Morning.

Not much time to prepare the slide, so I’ll go with some pointers.

Volume of tank ------- 48 litres

Volume of water in tank ------- 8 litres (1/6)

At 0932h , water in tank ------- 8 + (3*2) ------- 14 litres

From 0932h to 0943h, water flowing from tap X ----- 11*3 ------ 33 litres
14 + 33 ------- 47 litres

But the tank was 75% filled with water, so water had been drained out due to tap Y .

75% of 48 litres ------ 36 litres

47 – 36 ------- 11

11/11 ------ 1, hence water drain out rate from tap Y is 1 litre/minute.

From 36 litres to 48 litres, remember tap X adds 3 litres/min and tap Y drains 1 litres/min, so the net flow of water into tank is 2 litres/min.

12/2 ------- 6 minutes

From 0943h add 6 minutes, we’ll have 0949h

Best wishes

[Essential]

Good afternoon Tianzhu, need your kind help for this question.

Eugene, Freddy and George had some playing cards. Freddy had 200 more playing cards than Eugene. George had 3/4 the number of cards Freddy had. After George lost 1/6 of his cards to Eugene, he had 320 fewer cards than Eugene. What was the ratio of the number of cards Eugene had to the number of cards Freddy had to the number of cards George had in the end?