Q&A - PSLE Math

[jonaandr]

please help to solve the below 2 questions.


1. There were some balls in Boxes A,B and C. For every 3 balls in Box A, there were 7 balls in Box. For every 5 balls in Box B, there were 6 balls in Box C. After 48 balls were transferred from Box C to Box A, the ratio of the number of balls in Box A to the number of ball in Box B to the number of balls in Box C became 19:35:38. Find the total number of balls in the three boxes.

2. A motorcyclist travelle from Town A to Town B. It passed a taxi travelling from Town B to Town A. The taxi was traveling at a speed of 90 km/h. The motorcyclist reached Town B 1 1/2 hours after passing the taxi but the taxi was still 25 km away from Twon A. Both the motorcyclist and the taxi did not change their speeds throughout their journeys. If the motorcyclist took 4 hours to complete the shole journey, what was the distance between the two towns?

Thanks!

[charsen]

superksmum:

Hi please help on this question (Henry Park Prelim 2011, question 16).


Mr Lee took 7 hours to travel from Town A to Town B while Mr Wong took 8 hours to travel from Town B to Town A. Both of them did not change their spped throughout the journey. Both of them started off at the same time and moved towards each other. 3 hours later, they were 110km apart. What was the speed Mr Lee was driving?

Thank you.

Hi
In 3 hours, lee drove 3/8 of the journey.At the same time,wong took 3/7 of the journey.So,we should make the denominators 8 and 7 to be 56 since the distance in both is common.

Lee travelled 24U and wong travelled 21U.
56u-24U-21U=11U
11U-110km
1U-110/11=10km
Distance lee travelled--->10x24=240km
Lee's speed------>240/3=80km/h(ANS)

[charsen]

jonaandr:

please help to solve the below 2 questions.


1. There were some balls in Boxes A,B and C. For every 3 balls in Box A, there were 7 balls in Box. For every 5 balls in Box B, there were 6 balls in Box C. After 48 balls were transferred from Box C to Box A, the ratio of the number of balls in Box A to the number of ball in Box B to the number of balls in Box C became 19:35:38. Find the total number of balls in the three boxes.

2. A motorcyclist travelled from Town A to Town B. It passed a taxi travelling from Town B to Town A. The taxi was traveling at a speed of 90 km/h. The motorcyclist reached Town B 1 1/2 hours after passing the taxi but the taxi was still 25 km away from Town A. Both the motorcyclist and the taxi did not change their speeds throughout their journeys. If the motorcyclist took 4 hours to complete the shole journey, what was the distance between the two towns?

Thanks!

Hi
Q1. A:B B:C
3:7 5:6
x5 x5 x7 x7
A:B:C
15:35:42
19u-15u=4u
4u=48
1u=48/4=12
Total no. of Units----->92U-12x92=1104 balls (ANS)

Q2.Distance between meeting point and town A--->(90x 3/2)+25=135+25
=160km Time taken for the motorcyclist from town a to meeting point-->4h-1 1/2h
=2 1/2 h
Speed of the motorcyclist---->160/2 1/2h=64km/h
Distance between town A and town B------>64x4=256km(Ans)
cheers.

[charsen]

whitety:

Hi, need help on this qn.


Every Sat, Mabel will go for her usual exercise. If she runs up 32 steps and walks up 68 steps, she will take 184 seconds. If she runs up 50 steps and walks 50 steps, she will take 175 seconds. If she runs at the same rate throughout the whole exercise, how long will she take to run the 100 steps?


Thanks!

Hi
I have corrected the working:
184-175=9seconds
50-32=18 steps
18 steps-9seconds
Speed of mabel when she is walking--->1step-2seconds
2x50=100seconds
175-100=75 seconds
Speed od Mabel when she is running---->1step-1.5seconds
100 steps--->1.5x100=150 seconds(ANS)
cheers

[whitety]

charsen:

whitety:

Hi, need help on this qn.


Every Sat, Mabel will go for her usual exercise. If she runs up 32 steps and walks up 68 steps, she will take 184 seconds. If she runs up 50 steps and walks 50 steps, she will take 175 seconds. If she runs at the same rate throughout the whole exercise, how long will she take to run the 100 steps?


Thanks!

Hi
I have attempted this question.So, it could be wrong or correct.
184-175=9seconds
50-32=18 steps
18 steps-9seconds
1 step-2seconds
100 step-25 seconds(ANS)
cheers

Hi charsen,

Thanks for helping.

Answer is 150secs, which I can't get it.

[charsen]

Michaelia0816:

Tianzhu,

Pls help,

1)Each of the three cards shown below is printed with a different whole number.
The biggest number is 42. When these number are added two at a time, the sums are 57,64 and 77. What are the other 2 numbers?

2) A forty- page newspaper, which consists of only one section, has a sheet with page 9 and page 10 missing. What other pages are missing?

Pls done it by today as I am going to have math prelim the next day~.~

For Q2 , my solution may not be the best. But this is what I was able to arrive at.
Every Sheet of page has 4 pages. Num 1 appears in Pg1, Num 2 appears in Pg2, Num 38 in Pg3, Num 40 in Pg4 of the first sheet of paper. Continuing this way we'll get something like this where Odd pages will appear in Pg1 and Pg3. Even pages will hence be in Pg2, Pg4 of every sheet. Also, Pg1,2 will be consecutive numbers and Pg3,4 will be consecutive numbers.

Sheet# Pg1 Pg2 Pg3 Pg4
1 1 2 39 40
2 3 4 37 38
3 5 5 35 36

Let F be the number in first page and L be the number in the Pg4 and N be the sheet number.
If we look at the pattern above, we can see for a given N, F = (N-1)x2 +1.
Also, the sum of numbers in Pg1 + Pg4 is constant and is equal to 41
We can find number 9 appears in Pg1 of Sheet 5.
Remaining pages of Sheet 5 (missing sheet)
Pg2 --> number 10
Pg4 --> 41 -9 = 32
Pg3 --> 32-1 = 31

Missing pages beside 9, 10 are 31 and 32

[superksmum]

charsen:

superksmum:

Hi please help on this question (Henry Park Prelim 2011, question 16).


Mr Lee took 7 hours to travel from Town A to Town B while Mr Wong took 8 hours to travel from Town B to Town A. Both of them did not change their spped throughout the journey. Both of them started off at the same time and moved towards each other. 3 hours later, they were 110km apart. What was the speed Mr Lee was driving?

Thank you.

Hi
In 3 hours, lee drove 3/8 of the journey.At the same time,wong took 3/7 of the journey.So,we should make the denominators 8 and 7 to be 56 since the distance in both is common.

Lee travelled 24U and wong travelled 21U.
56u-24U-21U=11U
11U-110km
1U-110/11=10km
Distance lee travelled--->10x24=240km
Lee's speed------>240/3=80km/h(ANS)

:thankyou: charsen

[charsen]

catddy2002:

Hi,


Pls help to solve these 2 questions:

1) At a party, there were some balloons, 40 balloons burst and 25% of the remaining ballons flew away. If only 2/3 of the balloons were left, how many balloons were there at first?

2) Jarmanye planned to cycle from Town A to Town B. If she cycled at 20km/h, she would reach Town B at 2 pm. If she cycled at 12 km/h, she would reached Town b at 3.30 pm. What was the distance between Town A and Town B?

Thanks

Hi
Q1.Equating 75% of remainder and 2/3 of total.Equalizing numerators,
3/4 of remainder=2/3 of total
6/8 of remainder = 6/9 of total
Total no. of balloons---->9U
9U-8U=1U
1u=40
9u=40x9=360 balloons(ANS)

Q2.Imagine there are 2 persons,A and B.A is cycling at 20km/h and B is travelling at 12km/h.The difference in speed is 8km/h.When A reached Town B at 2.00p.m,the difference in distance is 12x1 1/2=18km.

18/8=2 1/4h
Distance between town a and b------>20x2 1/4=45km(ANS)

[tianzhu]

2DMommy:

Please help me with these :


Find the sum of 35 + 37 + 39 + 41 + 43 ........ + 231 + 233.

What is the short cut to this question ?

Thank you.

Hi

It may not be the shortest way, but this is my preferred way as students would be using the very familiar way of find the sum of odd numbers starting from 1.

First find the sum of 1 + 3 ………… 233

Number of odd numbers ------- (233+1)/2 ------ 117

Sum of odd numbers ------- 117*117 ------- 13689

Then find the sum of odd numbers from 1 + 3 ……… 33

Number of odd numbers ------- (33+1)/2 ------ 17

Sum of odd numbers ------- 17*17 ------ 289

Sum of 35 + 37 + 39 + 41 + 43 ........ + 231 + 233 ------- 13689 – 289 ------- 13400

Another possible way, almost similar to find the sum of even numbers from 1 to 100.

Number of odd numbers ------- (233+1)/2 ------ 117

Number of odd numbers ------- (35+1)/2 ------ 18

117 - 18 ------ 99

99 + 1 ------ 100

100/2 ------ 50

Pair up the numbers.

233 + 35 ------ 268

231 + 37 ------- 268

268*50 ------- 13400

Best wishes

[catddy2002]

charsen:

catddy2002:

Hi,


Pls help to solve these 2 questions:

1) At a party, there were some balloons, 40 balloons burst and 25% of the remaining ballons flew away. If only 2/3 of the balloons were left, how many balloons were there at first?

2) Jarmanye planned to cycle from Town A to Town B. If she cycled at 20km/h, she would reach Town B at 2 pm. If she cycled at 12 km/h, she would reached Town b at 3.30 pm. What was the distance between Town A and Town B?

Thanks

Hi
Q1.Equating 75% of remainder and 2/3 of total.Equalizing numerators,
3/4 of remainder=2/3 of total
6/8 of remainder = 6/9 of total
Total no. of balloons---->9U
9U-8U=1U
1u=40
9u=40x9=360 balloons(ANS)

Q2.Imagine there are 2 persons,A and B.A is cycling at 20km/h and B is travelling at 12km/h.The difference in speed is 8km/h.When A reached Town B at 2.00p.m,the difference in distance is 12x1 1/2=18km.

18/8=2 1/4h
Distance between town a and b------>20x2 1/4=45km(ANS)

Thanks Carsen! :thankyou: