Q&A - PSLE Math

[tianzhu]

pixiedust:

Hi all,


I can work out the Mary and Charles as the clue given is 'spent 4/5 as much'.
However, for the first burning candles question, I have difficulties with the burning rate ( u and p, I am ok).

Candle A -> 1hr 1/5 of candle burnt
Candle B -> 1hr 1/4 of candle burnt
why burning rate is A:B 4:5 ?

something similar to inversely proportional for speed questions ?

Hi

The candles A and B are of equal length.

A common multiple of 4 and 5 is 20.

Assuming the candle is 20 units long.

20/5 ------ 4 units (A)

20/4 ------ 5 units (B)

Hence A:B ------ 4:5

Best wishes

[MathIzzzFun]

kiasuaunt:

MathIzzzFun:

The candles solution looks so abstract...prob coz I donch have any heuristic background.


Building on what TZ has provided, I looked at it from another angle.

Let length of both candles by 20U.

Rate of burning for A & B are 4U/hr and 5U/hr respectively.

If T is the time taken, then

Length of A left = 20 - 4U*T
Length of B left = 20 - 5U*T

Since A is twice as long,

2*[20 - 5U*T] = 20U - 4U*T
=> 40U -10U*T = 20U - 4U*T
=> 20U = 6U*T
=> T = 20/6 = 3 1/3

hi

If we see the question as similar to this - http://www.flickr.com/photos/62167097@N02/5703951396/in/photostream, then it would not be as confusing.

or another question:
\"Mary and Charles had the same amount of money. After Mary spent 4/5 as much as Charles, Mary had twice as much as Charles had left. What fraction of Mary's money did she spend?\"

cheers.

What's the ans? Thanks.

Hi

the 3 questions can be solved using the \"same gap/diff\" concept.

Q1. Candle A and Candle B are of the same length. Candle A, which is broader, can burn for 5h while Candle B, the thinner candle, can burn for 4h. If both candles are lighted at the same time, how long does it take for Candle A to be twice as long left as Candle B?

The difference between burnt length of A & B is equal to the difference between remaining length of A &B

Burnt length of A : B --> 4 : 5 (diff of 1)
Remaining length of A : B --> 2 : 1 (diff of 1)
Total length of A = 6u = Total length of B
Time taken --> 4u/6u x 5h = 3 ⅓ h = 3h 20min

The remaining length of Candle A will be twice that of Candle B after 3h 20min.

Q2. Two candles of the same height are lit at the same time. The first candle takes 5h to burn completely. The second candle takes 4h to burn completely. If each candle burns at a constant rate, how long does it take, in hours, for the height of the first candle to be four times that of the second candle?

The difference between burnt length of A & B is equal to the difference between remaining length of A &B

Burnt length of 1st candle : 2nd candle --> 4 : 5 (diff of 1),
Remaining length of 1st candle : 2nd candle --> 4 : 1 (diff of 3),

Make the difference the same (3u):
Burnt length of 1st candle : 2nd candle --> 12u : 15u (diff of 3u),
Remaining length of 1st candle : 2nd candle --> 4u : 1u (diff of 3u),

Total length of A = 16u = Total length of B
Time taken --> 12u/16u x 5h = 3 ¾ h = 3h 45 min

The remaining length of 1st candle will be 4 times that of 2nd candle after 3h 45min.

Q3. Mary and Charles had the same amount of money. After Mary spent 4/5 as much as Charles, Mary had twice as much as Charles had left. What fraction of Mary's money did she spend?

The difference between Mary’s and Charles’s spending equal to the difference between the amount Mary and Charles had left.

Mary’s spending : Charles’s spending --> 4 : 5 (diff of 1)
Mary’s remaining amount : Charles’s remaining amount --> 2 : 1 (diff of 1)

Total amount each had --> 6u
Mary’s spending / Total --> 4u/6u = 2/3

Mary spent 2/3 of her money.

cheers.

[Nebbermind]

After much :frustrated: , I finally figure out why 1 unit = 1 P! :oops:

[kiasuaunt]

When Donald cycles from home to the park and back home, he will take half an hr. If he cycles to the park from home and runs back,he will take an hr. How long will he take to run both ways at the same speed? Thanks.

[Neat]

Hi!


Please help to solve the question:

The ratio of the number of males to the number of females at a performance is 5:7. 1/4 of the males and 3/4 of the females are children. What is the ratio of the number of adults to children? Express your answer in simplest form.

Thanks

[tech_nomax]

At Station A, the ratio of the number of children to the number of adults on a train was 4:5. At the next station, 12 children alighted and 10 adults boarded the train. The ratio of the number of children to the number of adults on the train then became 7:10. How many children were on the train at first?

[mum ks]

Neat:

Hi!


Please help to solve the question:

The ratio of the number of males to the number of females at a performance is 5:7. 1/4 of the males and 3/4 of the females are children. What is the ratio of the number of adults to children? Express your answer in simplest form.

Thanks

males: females=5:7 =>20:28
¼= 20 , ¾=60
Children = 60-28=32
Ratio of the no of adults to children = 48:32= 3:2

[Neat]

mum ks:

Neat:

Hi!


Please help to solve the question:

The ratio of the number of males to the number of females at a performance is 5:7. 1/4 of the males and 3/4 of the females are children. What is the ratio of the number of adults to children? Express your answer in simplest form.

Thanks

males: females=5:7 =>20:28
¼= 20 , ¾=60
Children = 60-28=32
Ratio of the no of adults to children = 48:32= 3:2

Thanks mum ks for your quick response.

However, the answer given is 11:13.

Regards

[MathIzzzFun]

Neat:

Hi!


Please help to solve the question:

The ratio of the number of males to the number of females at a performance is 5:7. 1/4 of the males and 3/4 of the females are children. What is the ratio of the number of adults to children? Express your answer in simplest form.

Thanks

Hi

ratio of males : females --> 5 : 7 --> 20 : 28
ratio of boys: men --> 5:15 (**1/4 of 20 : 3/4 of 20)
ratio of girls :women --> 21:7 (**3/4 of 28 : 1/4 of 28)
So,
ratio of adults : children --> 22: 26 = 11 : 13

cheers.

[MathIzzzFun]

kiasuaunt:

When Donald cycles from home to the park and back home, he will take half an hr. If he cycles to the park from home and runs back,he will take an hr. How long will he take to run both ways at the same speed? Thanks.

Hi

what (which part of the journey) remains the same ? --> cycle from home to park

what (which part of journey) changed ? --> cycle from park to home for 1st scenario, run from park to home for 2nd scenario

this means that the extra half an hour \"comes\" from the change ie running from park to home takes 1/2 h more than cycle from park to home.....can you complete the solution ?

cheers.