Q&A - PSLE Math

[tianzhu]

Winx5015:

Hi, can anyone help to solve this question.


In a hall, 3/5 of the pupils were girls. After some of the boys left the hall, the ratio of the number of girls to the number of boys increased to 5:2.
(a) If there were 36 boys left, how many pupils were there at first?
(b) At the beginning, the ratio of the number of girls who were in red T-shirts to those in black T-shirts was 4:5. 20% of the girls were in blue T-shirts. The number of girls in black T-shirts was the same as the number of boys in black T-shirts. If 20% of the remaining boys were in red T-shirts, how many boys were in blue T-shirts?

Thanks!

Hi

You may use MD or UM.

Before

B:G ----- 2:3 -------- 10:15

After

B:G ----- 2:5 ------ 6:15

The number of girls remains the same before and after. Make the number of units showing girls the same.

6 units ------ 36

1 unit ------ 6

Number of pupils @ first -------- 25*6 ------- 150

Number of girls@first ------ 15*6 ------- 90

Number of girls in blue T-shirts ------- 18 (20% of 90)

90 – 18 ------ 72

Girls in red T shirt: Girls in black T shirt ------- 4:5 -------- 32:40

The number of girls in black T-shirts was the same as the number of boys in black T-shirts.

Number of boys in black T shirt ------- 40

Number of boys@first ----- 60

60 – 40 ------- 20

Number of boys in red T shirt ------ 20% of 20 -------- 4

Number of boys in blue T shirt ------- 20 – 4 ------- 16

Best wishes

[tianzhu]

kwcllf:

Tank A, base measuring 60cmx10cm and height 40cm is empty. Tank B, base measuring 50cmx20cm and height 36cm, is 1/3 filled with water. Water is poured into the two tanks at the same time at a rate of 1.2 litres per minute.


How long it take for the height of the water to be the same in both tanks?

Thanks!

Hi

1 litres ------- 1000 cubic cm

1.2 litres/min ------ 1200 cubic cm/min

Tank A

Base area ------- 600 sqcm

In 1 min, the increase in height ------- 1200/600 ------- 2 cm

Tank B

Base area ------- 1000 sq cm

In 1 min, the increase in height ------- 1200/1000 ------- 1.2 cm

Height of water in tank B ------- 12 cm (1/3 filled)

Difference in height -------- 2 – 1.2 ------- 0.8

Time taken for height of the water to be the same in both tanks ------- 12/0.8 -------- 15 minutes

Best wishes

[kwcllf]

Thank you, Tianzhu :thankyou:

[peggy]

Tianzhu,


Thanks for your answer. Much appreciated.

Have a great weekend !

[Tiramisu Coco]

Hi, need help for this qtn.

Thank u.

http://www.flickr.com/photos/82618212@N07/7568230484

[Tiramisu Coco]

Hi, pls help with this qtn. Thks!

http://www.flickr.com/photos/82618212@N07/7568316568

[tianzhu]

Tiramisu Coco:

Hi, need help for this qtn.

Thank u.

http://www.flickr.com/photos/82618212@N07/7568230484

Hi

Good Morning.

Where is this question from?

It should be a breeze for secondary school students who have knowledge about tangential properties.

For primary schools, it might pose some challenges.

I think one way is show is to use a pair of compasses, draw two arcs from the centre of the circle to touch the longest side of the triangle (30 cm), say at a point X.

(24 – r ) + (18 – r) ------- 30

r + r ------- 42 – 30

r ------- 12/2 ------- 6

Try it out.

Hope this helps.

Best wishes

[Tiramisu Coco]

tianzhu:

Tiramisu Coco:

Hi, need help for this qtn.

Thank u.

http://www.flickr.com/photos/82618212@N07/7568230484

Hi

Good Morning.

Where is this question from?

It should be a breeze for secondary school students who have knowledge about tangential properties.

For primary schools, it might pose some challenges.

I think one way is show is to use a pair of compasses, draw two arcs from the centre of the circle to touch the longest side of the triangle (30 cm), say at a point X.

(24 – r ) + (18 – r) ------- 30

r + r ------- 42 – 30

r ------- 12/2 ------- 6

Try it out.

Hope this helps.

Best wishes

Hi Tianzhu,
Thks for your solution.
Pls enlighten why is
(24-r)+(18-r) --- 30?

Thks!

[tianzhu]

Tiramisu Coco:

Hi, pls help with this qtn. Thks!

http://www.flickr.com/photos/82618212@N07/7568316568

Hi

This is an interesting question.

It appears wordy and lengthy, so students have to read with care. Apply your knowledge of Distance ------ Speed* Time with a bit of reasoning and you should be on the way to the solution.

The 15 minutes was saved because John’s mum did not need to travel the distance equal to the circumference of the circle.

Divide the circle into 3 parts (120 degrees).

15/3 ------ 5

John’s mum saved 5 minutes (X to school)

Hence , John’s mum travelled for 20 minutes when she met John at X.

12.35pm -------- 12.55pm

John travelled for 25 minutes (1230 ----- 1255)

25/60*6 ------ 2.5 km

John travelled for 2.5 km.

For part b, draw a timeline

From 12.35pm. add 40 minutes

12.35 ------ 12.55 -------- 1.15

5 minutes ------- 5/60 ------ 1/12h

John’mum’s speed ------- 2.5*12 ------- 30km/h

Best wishes

[tianzhu]

Tiramisu Coco:

Hi Tianzhu,
Thks for your solution.
Pls enlighten why is
(24-r)+(18-r) --- 30?

Thks!

Hi

This question is pretty interesting.

This is a right angled triangle.

May I suggest you take out a pair of compasses and draw the arcs(points where the circle touches the triangle at right angles).

The two arcs meet the same point X on the longest side of the triangle.

After drawing, you’ll see why (24-r) + (18-r) add up to be equal to 30.

Best wishes