Q&A - PSLE Math

[wkong]

Another Maths question that I need advice:


In the 2 classes 6A and 6B, the total number of girls was 100% more than the total number of boys. The ratio of boys to girls in 6A was 3:4 and the ratio of boys to girls in class 6B was 1:6. If there were 8 more girls in class 6A than class 6B, find the number of pupils in class 6A.


Thanks,
wkong

[raghupavithra]

Wen Si used a piece of wire to form an outline of a flower as shown below.








She bent the 3 petals of the flowers into 6 identical quater arcs of radius 7 cm each. The perimeter of the stalk of the flower was 19 cm. If 1 m of the wire cost $0.80, what was the cost of the wire she had used for 5 flowers?



(Take pie = 22/7​ )

[raghupavithra]

A school library had only English, Chinese and Malay books… 55% of the books were English books. 20% of the remainder was Malay books and the rest were Chinese books. The number of Malay books was 432 less than the number of Chinese books. Find the total number of books in the library.

[KRR]

CoffeeCat:

KRR:

Can u help me with this problem.


Two boys A and B shared some chocolate bars.

If A gives 8 bars of chocolate to B,
A will have 6 times as many chocolates as B.

However, if B gives 12 bars of chocolate to A,
B will have 1/11 of the number of bars A has.

Find the total number of chocolate bars they had.

Thanks in advance.
KRR

Under the \"Challenging Problems Made Easy\" this type of problem is called
Internal Transfer with Unchanged Total.

Most of the \"transfer\" questions can be solved by ratio, the crux here is that the total remains unchanged.
If A gives 8 to B
A : B : Total
6 : 1 : 7
72 : 12 : 84

If B gives 12 to A
A : B : Total
11 : 1 : 12
77 : 7 : 84

We \"manipulate\" or multiply the ratios so that the total is the same in both scenarios.
In reality the amt of chocs A has is somewhere between 72 and 77 units.
77-72 = 5 units --> 12 + 8 = 20
So the total amt of chocs they have is 84 units =...

It was so clear, thank you very much.
KRR

[CoffeeCat]

raghupavithra:

A school library had only English, Chinese and Malay books.. 55% of the books were English books. 20% of the remainder was Malay books and the rest were Chinese books. The number of Malay books was 432 less than the number of Chinese books. Find the total number of books in the library.

In the world of model-drawing, we need the units representing the different types of books to be the same (noticed that malay books is expressed in terms of the remainder, not the total).
55% of the books -> Englsh
20% * 45% = (1/5 * 45%) = 9 % of the books -> Malay
100% - 55% - 9% = 36% of the books -> Chinese
36% - 9% = 27 % of the books --> 432
1% of book --> 432/27 = 16
Total number -> 1600

[CoffeeCat]

wkong:

Hi All,


Would like to seek advice for the following question:

At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.

a) What time did they pass each other?
b) If John took another 3 minutes to reach Point B, what time would Mary reach Point A?


Thanks,
wkong

If u draw the \"Distance line\", just a straight line from A to B, with the midpoint, and another point (call it D) , where D is between midpoint and B, you will see that line segment AD represent distance travelled by John while DB represent distance travelled by Mary.
Currently D is 300m away from midpoint. Now we are given the difference in speed, using DST formula, in order to find time, we need difference in distance. So by reflecting the point D about the midpoint, call the new point D', you will find that D'D represents the difference in distance, namely 600m = 0.6km.
Time taken = 0.6 / 4 = 0.15 hour = 9 mins

Part B)
This is an inverse speed ratio question, 1 of the most challenging type of speed question that can appear for p6 school syllabus.
Notice that John travel DB in 3 mins
while Mary travel DB in 9 mins (from part A).
Intuitively Mary travel 3 times as slow as John and hence will always take 3 times as much time as John to cover the same distance.
So if John travel from A to B in 3+ 9 = 27 min, Mary will travel from B to A in 3*27 = 81 mins.

[wkong]

CoffeeCat:

wkong:

Hi All,


Would like to seek advice for the following question:

At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.

a) What time did they pass each other?
b) If John took another 3 minutes to reach Point B, what time would Mary reach Point A?


Thanks,
wkong

If u draw the \"Distance line\", just a straight line from A to B, with the midpoint, and another point (call it D) , where D is between midpoint and B, you will see that line segment AD represent distance travelled by John while DB represent distance travelled by Mary.
Currently D is 300m away from midpoint. Now we are given the difference in speed, using DST formula, in order to find time, we need difference in distance. So by reflecting the point D about the midpoint, call the new point D', you will find that D'D represents the difference in distance, namely 600m = 0.6km.
Time taken = 0.6 / 4 = 0.15 hour = 9 mins

Part B)
This is an inverse speed ratio question, 1 of the most challenging type of speed question that can appear for p6 school syllabus.
Notice that John travel DB in 3 mins
while Mary travel DB in 9 mins (from part A).
Intuitively Mary travel 3 times as slow as John and hence will always take 3 times as much time as John to cover the same distance.
So if John travel from A to B in 3+ 9 = 27 min, Mary will travel from B to A in 3*27 = 81 mins.

Thanks for the help.

[CoffeeCat]

wkong:

Another Maths question that I need advice:


In the 2 classes 6A and 6B, the total number of girls was 100% more than the total number of boys. The ratio of boys to girls in 6A was 3:4 and the ratio of boys to girls in class 6B was 1:6. If there were 8 more girls in class 6A than class 6B, find the number of pupils in class 6A.


Thanks,
wkong

As usual to solve using ratios, we need to convert the units to be that of the same size. (The problem is A and B are of different sizes, we need to find their size relative to each other)
To accomplish this we can use algebra or guess & check.



Let A and B represent the number of students in 6A & 6B respectively.
Then 3/7 * A + 1/7 * B = boys
4/7 *A + 6/7 * B = girls
Notice girls = 2* boys
So 6/7 * A + 2/7 * B = 4/7 * A + 6/7 *B
2/7 * A = 4/7 * B
A = 2B

Now we can use ratios to finish the question
6A
B : G : Total
3 : 4 : 7
6 : 8 : 14
6B
B : G : Total
1: 6 : 7
(Check that 8+ 6 = 14 is 2 times (6+1) , satisfying that \" the total number of girls was 100% more than the total number of boys.\")
2 units -> 8
6A -> 14 units -> 56

[wkong]

CoffeeCat:

wkong:

Another Maths question that I need advice:


In the 2 classes 6A and 6B, the total number of girls was 100% more than the total number of boys. The ratio of boys to girls in 6A was 3:4 and the ratio of boys to girls in class 6B was 1:6. If there were 8 more girls in class 6A than class 6B, find the number of pupils in class 6A.


Thanks,
wkong

As usual to solve using ratios, we need to convert the units to be that of the same size. (The problem is A and B are of different sizes, we need to find their size relative to each other)
To accomplish this we can use algebra or guess & check.



Let A and B represent the number of students in 6A & 6B respectively.
Then 3/7 * A + 1/7 * B = boys
4/7 *A + 6/7 * B = girls
Notice girls = 2* boys
So 6/7 * A + 2/7 * B = 4/7 * A + 6/7 *B
2/7 * A = 4/7 * B
A = 2B

Now we can use ratios to finish the question
6A
B : G : Total
3 : 4 : 7
6 : 8 : 14
6B
B : G : Total
1: 6 : 7
(Check that 8+ 6 = 14 is 2 times (6+1) , satisfying that \" the total number of girls was 100% more than the total number of boys.\")
2 units -> 8
6A -> 14 units -> 56

Thanks again.

[atutor2001]

raghupavithra:

2/3​ of X is equal to 1/5​ of Y. Find the value of 80% of Y if X is 930. how to do this sum

Hi

Step 1 : Find the ratio of x :y
2/3 of x = 1/5 of y
2/3 of x = 2/10 of y
The ratio of x : y = 3 : 10 (the denominators of the fractions)

Step 2 : Find y
3 unit is 930
1 unit is 930/3 = 310
10 units (y) = 310 x 10 = 3100

Step 3 : Find 80% of y
80/100 x 3100 = 2480 (answer)