Q&A - PSLE Math

[JadeDry]

Dharma:

7/3 refers to 7/3 hrs ( 2 hrs 20 mins ) which is the total cycling time

Thank you Dharma.

I have another question and would greatly appreciate your assistance on this one as well.

Ahmad and Kumar together can paint a house in 12 days. Kumar and Chong beng together can complete the same job in 15 days while Ahmad and Chong beng together will take 20 days to paint the same house. How many days will it take Ahmad, Kumar and Chong beng to complete the job together?

These are my workings so far:

Ahmad= A

Kumar= K

Chong Beng= C

A+K = 12 days = 8 1/2 to 3 1/2

K+C= 15 days = 3 1/2 + 11 1/2

Therefore A:K:C = 8 1/2: 3 1/2 : 11 1/2 = 17:7:23

Therefore Speed rate = K:A:C

= 3 11/119 : 1 42/119 : 1

100% = 4 53/119

therefore 3 11/119 p= (100/1) x (119/518) x (368/119)= 72 3488/30 821

12 x 72 3488/30 821= approximately 8 13/20

(8 13/20) / (3 11/119) = Approximately 2.8

12- 2.8= 9.2 days

However I understand that the answer should be 10. I would greatly appreciate it if you could point out the error in my working.

[iFruit]

JadeDry:

Dharma:

7/3 refers to 7/3 hrs ( 2 hrs 20 mins ) which is the total cycling time

Thank you Dharma.

I have another question and would greatly appreciate your assistance on this one as well.

Ahmad and Kumar together can paint a house in 12 days. Kumar and Chong beng together can complete the same job in 15 days while Ahmad and Chong beng together will take 20 days to paint the same house. How many days will it take Ahmad, Kumar and Chong beng to complete the job together?

The trick (SOP) for work problems is that we reduce the work to unit rate.

Ahmad and Kumar together can paint a house in 12 days.--->Ahmad and Kumar together can paint 1/12 the house in 1 days.

A+K = 1/12 of house in a day
K+C= 1/15 of house in a day
A+C= 1/20 of house in a day

Adding all together

2(A+K+C) = 1/12+1/15/+1/20 = 1/5 in a day
A+K+C = 1/10 in a day

So they take 10 days to finish the job together.

HTH

[atutor2001]

JadeDry:

I have another question and would greatly appreciate your assistance on this one as well.

Ahmad and Kumar together can paint a house in 12 days. Kumar and Chong beng together can complete the same job in 15 days while Ahmad and Chong beng together will take 20 days to paint the same house. How many days will it take Ahmad, Kumar and Chong beng to complete the job together?

[i]These are my workings so far:

Ahmad= A

Kumar= K

Chong Beng= C

A+K = 12 days = 8 1/2 to 3 1/2

K+C= 15 days = 3 1/2 + 11 1/2

I think the error lies with the assumption that K will spend the same amount of time (i.e. 3 1/2 days) regardless whether he is painting with A or C.

Rightfully, K should spend longer time when painting with C than when painting with A because the total time taken with C is longer. The amount of time K spent is dependent of the total time taken - the longer the total time taken, the more time K will need to spend painting.

[iFruit]

atutor2001:

JadeDry:

I have another question and would greatly appreciate your assistance on this one as well.

Ahmad and Kumar together can paint a house in 12 days. Kumar and Chong beng together can complete the same job in 15 days while Ahmad and Chong beng together will take 20 days to paint the same house. How many days will it take Ahmad, Kumar and Chong beng to complete the job together?

[i]These are my workings so far:

Ahmad= A

Kumar= K

Chong Beng= C

A+K = 12 days = 8 1/2 to 3 1/2

K+C= 15 days = 3 1/2 + 11 1/2

I think the error lies with the assumption that K will spend the same amount of time (i.e. 3 1/2 days) regardless whether he is painting with A or C.

Rightfully, K should spend longer time when painting with C than when painting with A because the total time taken with C is longer. The amount of time K spent is dependent of the total time taken - the longer the total time taken, the more time K will need to spend painting.

atutor2001 is right. You cannot apportion 3 1/2 days to K and 8 1/2 days to A. They both work for 12 days, just that amount of work they do is different.

[JadeDry]

Many thanks, your assistance is greatly appreciated.

[CTong]

Mr Tan had some white and some black buttons. 60% were white. He bought another 120 buttons. Now, the percentage of white buttons became only 40% of the total. How many white buttons did he have at first?


Dexter is given $7.50 more pocket money than Dee Dee each week. Each of them spends $9.50 every week and saves the rest. When Dexter saves $55.50, Dee Dee saves $18. How much pocket money does Dexter receive each week?

[tianzhu]

CTong:

Mr Tan had some white and some black buttons. 60% were white. He bought another 120 buttons. Now, the percentage of white buttons became only 40% of the total. How many white buttons did he have at first?


Dexter is given $7.50 more pocket money than Dee Dee each week. Each of them spends $9.50 every week and saves the rest. When Dexter saves $55.50, Dee Dee saves $18. How much pocket money does Dexter receive each week?

Hi

A quick one for Q2

Dexter ----- 55.50
Dee Dee ----- 18
Difference in savings ------ 37.50

Dexter saves $7.50 more per week
Number of weeks to achieve $37.50 ------ 37.5/7.5 ------5

Amount of savings per week for Dexter ------- 55.50/5 ------ 11.10

Amount of pocket money per week for Dexter ------- 11.1+9.50 -------20.60

As for Q1, there may be some missing information, you may wish to check the source again.

Best wishes

[Brenda10]

Hi Tianzhu


We came across this similar quesiton on AI Tong SA2009 SA2 Q17.

A seamstress had some white and some black buttons. 60% of the buttons were white. He bought another 120 buttons. Now, the percentage of white buttons became only 40% of the total. How many white buttons did he have at first?


The following was dd working:

W:B
3:2 (Before)
Plus 120
4:6 (After)

4-3=1
6-2=4
1+4=5
120/5=24
24*3= 72

There are 72 white marbles at frist.

So happen her answer match the answer sheet given, therefore I just presume her working is correct.

Thank you

[tianzhu]

Hi Brenda10


I think there will be mutiple answers for this question(aitong).

Your girl's answer is one of many possibilties.

She used 4:6 as the after ratios in her solution.

Try 8:12(40% of the total) and you will get a different answer.
Again, you may try 16:24 and you'll get another answer.

The list goes on,and different after ratios which satisfy the condition(40% of the total) will give a different answer.

Now compare the original question with this one

40% of the animals on a farm were chickens and the rest were ducks. When another 104 chickens and ducks were bought, the number of chickens was increased by 20% and the number of ducks was increased by 30%.
(a) Find the number of chickens on the farm at first, and
(b) the number of ducks on the farm after the increase.

You may want to let your girl try out the new question and observe the difference.

Best wishes

[Brenda10]

tianzhu:

Hi Brenda10


I think there will be mutiple answers for this question(aitong).

Your girl's answer is one of many possibilties.

She used 4:6 as the after ratios in her solution.

Try 8:12(40% of the total) and you will get a different answer.
Again, you may try 16:24 and you'll get another answer.

The list goes on,and different after ratios which satisfy the condition(40% of the total) will give a different answer.

Now compare the original question with this one

40% of the animals on a farm were chickens and the rest were ducks. When another 104 chickens and ducks were bought, the number of chickens was increased by 20% and the number of ducks was increased by 30%.
(a) Find the number of chickens on the farm at first, and
(b) the number of ducks on the farm after the increase.

You may want to let your girl try out the new question and observe the difference.

Best wishes

Hi Tianzhu

Noted and thank you for your highlight.

Have a nice day.