Q&A - PSLE Math

[wilburlim]

1760 children took part in a run last year. This year, the number of boys increased by 20% while the number of girls decreased by 20%. As a result, the number of girls became twice as many as the number of boys this year.
(a) How many boys took part in the run last year?
(b) What is the percentage decrease in the number of children who took part in the run this year?

Start with boys =5u last year. 5u selected because it's easier to work with a 20% increase.

This year the boys = 1.2 X 5u = 6u , i.e 20% increasse from 5u
This year the girls= 12u , i.e. twice of boys this year.

Girls this year is 80% of girls last year
80% => 12u
100% => 12u/0.8 = 15u <-last year girls

5u + 15u = 1760
20u =1760
u = 88

a) Last year boys = 5u = 5(88) = 440#

b) Total participants for last year = 20u
Total paticipants for this year = 6u+12u = 18u
Reduce by 2u
% reduction = 2u/20u X 100 = 10% ###

Hi, thanks for the reply! But is there a easier way to solve this? I don't understand the 5u for boys at first.

[questionable_i]

Can anyone help me with these questions? in advance.

Q1)


Q2)


Q3)


Q4)


Q5)


Q6)

[Ender]

1760 children took part in a run last year. This year, the number of boys increased by 20% while the number of girls decreased by 20%. As a result, the number of girls became twice as many as the number of boys this year.
(a) How many boys took part in the run last year?
(b) What is the percentage decrease in the number of children who took part in the run this year?

Start with boys =5u last year. 5u selected because it's easier to work with a 20% increase.

This year the boys = 1.2 X 5u = 6u , i.e 20% increasse from 5u
This year the girls= 12u , i.e. twice of boys this year.

Girls this year is 80% of girls last year
80% => 12u
100% => 12u/0.8 = 15u <-last year girls

5u + 15u = 1760
20u =1760
u = 88

a) Last year boys = 5u = 5(88) = 440#

b) Total participants for last year = 20u
Total paticipants for this year = 6u+12u = 18u
Reduce by 2u
% reduction = 2u/20u X 100 = 10% ###

Hi, thanks for the reply! But is there a easier way to solve this? I don't understand the 5u for boys at first.

5u is selected because 20% of 5u is just 1u.. Easier to work.
We can also select boys to be 10u at first if you want,, which will also work well with a 20% increase.
e.g Let last year boys be 10u,
This year boys will be 12u, i.e 20% increase,
This year girls will be 24u , i.e. twice of this year boys

80% =>24u
100%=> 24u/0.8 = 30u Last year girls

30u+10u = 1760
40u=1760
u = 44

a) 10u = 440 #
b) reduction by 40u - 36u = 4u
% reduction = 4u/40u X 100 = 10% ###

[alfretztay]

Can anyone help me with these questions? in advance.

Q1)


Q2)


Q3)


Q4)


Q5)


Q6)

Q1. Justina had 72 more Singapore stamps than Malaysia stamps. She gave away some Singapore and Malaysia stamps. The number of Singapore stamps she gave away was 3/4 of the number of Malaysia stamps she had at first. The number of Malaysia stamps she gave away was 1/2 the number of Singapore stamps she had at first. In the end, she had an equal number of each type of stamps, How many Singapore stamps did Justina have at first?

Before :
S : 4u + 72
M : 4u

After :
S : 4u + 72 - 3u = 1u + 72
M : 4u - 2u - 36 = 2u - 36

1u + 72 = 2u - 36
1u ------- 108
4u + 72 = 4 x 108 + 72 = 504

Ans : 504 Singapore stamps.


Q2. The number of toys cars Keith had was 1/5 the number of paper aeroplanes. After he gave 1/2 of his paper aeroplanes and 1/3 of his toys cars to his brother, he had 286 more paper aeroplanes than toy cars. (a) How many toy cars did Keith have in the end? (b) How many toy cars and paper aeroplanes did Keith have at first?

(a)

TC : PA
1 : 5
6u : 30u


TC : 6u - 2u = 4u
PA : 30u - 15u = 15u
15u - 4u = 11u ------- 286
1u ------- 286/11 = 26
4u ------- 26 x 4 = 104

(b)
6u + 30u = 36u
36u ------- 36 x 26 = 936

Alternatively,
6u ------- 26 x 6 = 156 (toy cars at first)
30u ------- 26 x 30 = 780 (paper aeroplanes at first)
780 + 156 = 936

Ans : (a) 104 toy cars ; (b) 936 toy cars and paper aeroplanes.


Q3. In a boutique, 40% of the clothing are dresses. 70% of the remainder are skirts and the rest are pants. There are 30 more skirts than dresses. After some dresses are sold, 25% of the remaining clothing in the boutique are dresses. How many dresses are there left in the boutique?

100 - 40 = 60 (remainder)
70% x 60 = 42 (skirts)
60 - 42 = 18 (pants)
42 - 40 = 2
2% ------- 30
1% ------- 30/2 = 15

42% ------- 15 x 42 = 630
18% ------- 15 x 18 = 270
270 + 630 = 900
100% - 25% = 75%
75% ------- 900
1% ------- 900/75 = 12
25% ------- 12 x 25 = 300

Ans : 300 dresses.



Q4.
Image
Area of circle with radius 56cm -------- (22/7) x 56 x 56 = 9856
9856/2.2 = 4480
3.5u x 5u = 17.5u^2
17.5u^2 -------- 4480
u^2 ------- 4480/17.5 = 256
256 = 16 x 16
1u ------- 16
3.5u ------- 16 x 3.5 = 56
5u ------- 16 x 5 = 80
(80 + 56) x 2 = 272

Ans : 272 cm.



Q5. Meng has a total of 1296 black and white buttons. He has 720 more black buttons than white buttons. He puts all the black buttons equally into empty black boxes and puts all the white buttons equally into empty white boxes. There are thrice as many black boxes as white boxes. Each black box contains 4 more buttons than each white box. How many buttons are there in each white box?

1296 - 720 = 576
576/2 = 288 (white)
288 + 720 = 1008 (black)
1008/3 = 336
336 - 288 = 48
48/4 = 12
288/12 = 24

Alternatively,
Total black buttons : 3u ------- (1296 + 720)/2 = 1008
1008/3 = 336
Total white buttons : 1u ------- 1008 - 720 = 288
336 - 288 = 48
48/4 = 12 (number of boxes in 1u)
Number of white buttons in 1 box = 288/12 = 24

Ans : 24 buttons.


Q6. The ratio of Isabellas savings tot Joannas savings was 9 : 8. Isabella and Joanna shared the cost of buying a birthday present for their grandmother in the ratio of 2 : 1 respectively. Isabella used up 2/3 of her savings to pay for her share of the present. Joanna was left with $150 after paying her share. (A) How much was Joanna's savings? (b) What was the cost of the present?

(a)
I : 9u - 2p = 3u = 9u - 6u
2p ------- 6u
1p ------- 3u
J : 8u - 1p = 8u - 3u = 5u
5u ------- 150
1u ------- 150/5 = 30
8u ------- 30 x 8 = 240

(b)
3p ------- 3 x 3u = 3 x 3 x 30 = 270

Ans : (a) $240; (b) $270.

[happy to be mum]

Can anyone help me to solve this Math question?

Ben had 40% more money than Susan. Joanne had 30% less the amount of money Ben had. If Joanne had $490, how much did Susan had?

[PiggyLalala]

Can anyone help me to solve this Math question?

Ben had 40% more money than Susan. Joanne had 30% less the amount of money Ben had. If Joanne had $490, how much did Susan had?

Susan -100%
Ben -140%

Ben - 100%
Joanne -70%
70% - $490
1% - $7
Ben: 100% -$700

Ben: 140% -$700
1% -$5
Susan:100% - $500

susan had $500.

[wilburlim]

I need help. Thanks!

Ashley was given a sum of money. She spent the same amount of money each day. She spent 2/7 of her money in 6 days. After another 5 days, she had $20 left. How much money did she have at first?

Town A and B were 360km apart. A car left Town A for Town B at 10.30p.m, at an average speed of 70km/h. At the same time, a van left Town B for A, travelling along the same road, at an average speed of 50km/h. At what time did the car and van pass each other?

[questionable_i]

Ashley was given a sum of money. She spent the same amount of money each day. She spent 2/7 of her money in 6 days. After another 5 days, she had $20 left. How much money did she have at first?

1 Day she spent (In fraction) --> 2/7 /6=1/21
How many days -->6+5=11 days
In 11 Days, she spent (In fraction) --> 1/21 x 11=11/21
Left (In fraction) -->1-11/21=10/21
10u -->$20
1u -->$20/10=$2
21u -->$2*21=$42

Ans: She have $42 at first.

[Ender]

I need help. Thanks!
Town A and B were 360km apart. A car left Town A for Town B at 10.30p.m, at an average speed of 70km/h. At the same time, a van left Town B for A, travelling along the same road, at an average speed of 50km/h. At what time did the car and van pass each other?

Distance to cover = 360km
Relative speed between car and van = 70 + 50 = 120km/h
Time taken till they meet, i.e both covered a total of 360km altogether = 360/120 = 3hr

Time => 10:30 pm plus 3 hr => 1:30 am ###

[wilburlim]

Someone help me for this question please.

The Robotics Club had twice as many pupils as the Science Club. The ratio of the number of girls to the number of boys in the Robotics Club was 4:1. The ratio of the number of girls to the number of boys in the Science Club was 2:3.
(a) Find the ratio of the number of girls in the Robotics Club to the number of girls in the Science Club.
(b) After 38 girls left the Robotics Club to join the Science Club, the ratio of the number of girls to the number of boys in the Science Club became 9:4. How many girls were in the Science Club in the end?