Q&A - PSLE Math

[Vanilla Cake]

tianzhu:

Thank you for your help.


David’s father picks him up from school every evening at 6 pm. One day, David was dismissed early at 5 pm. He walked home taking the same route that his father usually drives. When he met his father along the way he boarded the car and returned home 50 minutes earlier than usual. Given that his father drove at a constant speed and planned to reach the school at 6 pm sharp, how long, in minutes, had he walked before he was picked up by his father?

Source: Singapore Mathematical Olympiad for Primary Schools 2005 - Q25.

[Vanilla Cake]

tianzhu:

Thank you for your help.

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Source: Singapore Mathematical Olympiad for Primary Schools 2005 - Q26.

[JadeDry]

Hello again.


I have a question that I think I managed to solve but am not sure its correct. could you please point out any mistakes? (if any)

In a 100m race Edwin beats Beng Seng by 10m. The two boys plan to have another race. Edwin will start 10m behind the start line this time.

If both boys run at the same rate as before, who will win the race? Or is it a draw? If someone wins the race then he wins by how many meters?

Edwin= E

Beng Seng= B

E can run 100m in X seconds

B can run 90m in X seconds.

E can run 110m in (X+Y) seconds

B can run 100m in (X+Y) seconds

Therefore if E starts 10m behind the start line

E and B would be tied.


Thanks in advance for your help.

[tianzhu]

Hi


Try to turn words into picture.

You may draw a simple diagram to show the two runners. For the same period of time, Edwin covered 100m while Beng Seng ran 90m.Therefore, Edwin’s speed is faster.

Edwin -----100m
Beng Seng -----90m

Hence
Edwin ------10m
Beng Seng -----9m

In the second race, Beng Seng has a head start of 10m.

Therefore, Edwin will catch up with him at the 90m mark. From here, Edwin will complete the race first as he has a faster speed. He’ll be 1m ahead of Beng Seng when he reaches the ending point.

Best wishes

[JadeDry]

tianzhu:

Hi


Try to put words into picture.

You may draw a simple diagram to show the two runners. For the same period of time, Edwin covered 100m while Beng Seng ran 90m.Therefore, Edwin’s speed is faster.

Edwin -----100m
Beng Seng -----90m

Hence
Edwin ------10m
Beng Seng -----9m

In the second race, Beng Seng has a head start of 10m.

Therefore, Edwin will catch up with him at the 90m mark. From here, Edwin will complete the race first as he has a faster speed. He’ll be 1m ahead of Beng Seng when he reaches the ending point.

Best wishes

Thank you, that was very helpful.

[tianzhu]

JadeDry:

Thank you, that was very helpful.

Hi

You're welcome.

Best wishes

[JadeDry]

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

[iFruit]

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

Bill increased by 33 1/3 % means it increased by a third. So the total price after the mistake = 1 1/3 of total price before mistake = 4/3 of total price before mistake

Let cost of leather shoe = C
Then cost of canvas shoe = = C/2.5 = 2C/5

Number of pairs of leather shoes = 5
Let Number of pairs of canvas shoes = n

total cost before the mistake = 5C + n*2C/5 = C (5 + 2n/5)

total cost after the mistake = nC + 5*2C/5 = nC + 2C = C (n+2)

4/3 * C(5 + 2n/5) = C(n+2)

4/3 * (5 + 2n/5) = (n+2)

20 + 8n/5 = 3n + 6

14 = 3n - 8n/5 = 7n/5---> n =10

ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes = 10:5 = 2:1

HTH

[JadeDry]

iFruit:

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

Bill increased by 33 1/3 % means it increased by a third. So the total price after the mistake = 1 1/3 of total price before mistake = 4/3 of total price before mistake

Let cost of leather shoe = C
Then cost of canvas shoe = = C/2.5 = 2C/5

Number of pairs of leather shoes = 5
Let Number of pairs of canvas shoes = n

total cost before the mistake = 5C + n*2C/5 = C (5 + 2n/5)

total cost after the mistake = nC + 5*2C/5 = nC + 2C = C (n+2)

4/3 * C(5 + 2n/5) = C(n+2)

4/3 * (5 + 2n/5) = (n+2)

20 + 8n/5 = 3n + 6

14 = 3n - 8n/5 = 7n/5---> n =10

ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes = 10:5 = 2:1

HTH

Thanks, that helps a lot.

[tianzhu]

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

Hi

This is an interesting question, haven't seen such question from past years papers.

Best wishes