Q&A - PSLE Math

[Michaelia0816]

Ok!

[MathIzzzFun]

Michaelia0816:

Pls try not to use algebra, I am easily confused. Help with this Qn,


Motorist takes 1/2 h less than the usual time to travel from Town K to Town J when he increases his average speed by 10%. For a distance of 100km, he will take 1/3 h less than the usual time if his speed is 20% more than the average speed from Town K to Town J. Find the distance between Town K and Town J.

For a distance of 100km, he will take 1/3 h less than the usual time if his speed is 20% more than the average speed from Town K to Town J. - info provided in this sentence can be used to calculate the normal speed:

normal speed : 120% normal speed = 100 : 120 = 10 : 12
Time ratio to travel 100km at normal speed : 120% normal speed = 12u : 10u
2u --> 1/3h
12u --> 2h ie it takes 2h to cover 100 km at normal speed, so normal speed = 100km/2h = 50 km/h

Time to travel from town K to town J at
normal speed : 110% normal speed = 110 : 100 --> 11u : 10u
1u --> 1/2h (since it takes 1/2 h less to travel at 110% normal speed)
11u --> 5.5h, distance between town K and town J = 5.5h x 50 km/h = 275 km

cheers.

[Michaelia0816]

Pls help with this question,


A car travels from town P to town Q at a constant speed. When it increases its speed by 20%, the journey from P to Q takes 1 hour less than its usual time. When it travels at its usual speed for 100 km before increasing its speed by 30%, the journey also takes 1 hour less than usual. Find the distance between the two towns.

[Michaelia0816]

MathIzzzFun:

Michaelia0816:

Pls try not to use algebra, I am easily confused. Help with this Qn,


Motorist takes 1/2 h less than the usual time to travel from Town K to Town J when he increases his average speed by 10%. For a distance of 100km, he will take 1/3 h less than the usual time if his speed is 20% more than the average speed from Town K to Town J. Find the distance between Town K and Town J.

For a distance of 100km, he will take 1/3 h less than the usual time if his speed is 20% more than the average speed from Town K to Town J. - info provided in this sentence can be used to calculate the normal speed:

normal speed : 120% normal speed = 100 : 120 = 10 : 12
Time ratio to travel 100km at normal speed : 120% normal speed = 12u : 10u
2u --> 1/3h
12u --> 2h ie it takes 2h to cover 100 km at normal speed, so normal speed = 100km/2h = 50 km/h

Time to travel from town K to town J at
normal speed : 110% normal speed = 110 : 100 --> 11u : 10u
1u --> 1/2h (since it takes 1/2 h less to travel at 110% normal speed)
11u --> 5.5h, distance between town K and town J = 5.5h x 50 km/h = 275 km

cheers.

Why it is 2u? Sorry, actually I bit stupid, I am a bit slow in learning, especially in math.

[tianzhu]

Michaelia0816:

Pls help with this question,


A car travels from town P to town Q at a constant speed. When it increases its speed by 20%, the journey from P to Q takes 1 hour less than its usual time. When it travels at its usual speed for 100 km before increasing its speed by 30%, the journey also takes 1 hour less than usual. Find the distance between the two towns.

Hi

I don’t think this is a typical PSLE type of question.

Usual speed: New speed ----- 10:12 ------5:6

Usual time: New time -------6:5

1 unit ----- 1h

Usual time ------6 h

Now consider the second scenario.

Usual speed: New speed ----- 10:13

Usual time: New time -------13:10

3 units ------ 1

13 units ------ 13/3 or 4 1/3

6 – 4 1/3 ------ 1 2/3 (5/3)

5/3 ----- 100 km

6 ------ 100*6/5/3 ------- 360km

Best wishes

[kiasuaunt]

tianzhu:

peggy:

Kindly assist this 2012 SA 1 question.


There are 1000 students at the parade ground and indoor sports hall. 40% of the 600 students at the parade ground were girls. 60% of the students at the indoor sports hall were girls. After some students in both venues moved from one venue to the other, 30% of the students in the parade ground and 70% of the students at the indoor sports hall were girls. How many students were there in the indoor sports hall after the movement had taken place ?

Thank you.

Hi

This question has been discussed before.

Best wishes

http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&start=4330

http://farm7.static.flickr.com/6070/6154555481_a1f43e1359_z.jpg\">

Hi - don't understand this part: 7u+3u+30 = 480. How did u get +30 ? Sorry for being so slow.

Thank you.

[kiasuaunt]

Winx5015:

Hi, need help for the following questions.


(1). There were 40 red pens and 45 blue pens in Stall A. Stall B had 50 red pens and 15 blue pens. How many red pens must be moved from Stall B to Stall A so that 50% of the pens in Stall A and 75% of the pens in Stall B are red?

(2). In a library, 25% of the books were non-fiction books and the rest were fiction books. 7/10 of the non-fiction books and 3/10 of the fiction books were borrowed by some pupils. If 1600 books were borrowed, how many more fiction books than non-fiction books were there in the library at first?

(3). Ali and Ben had $150.30 at first. Ali gave 1/2 of his money to Ben. Ben then gave 2/5 of the total he had to Ali. In the end, each of them had the same amount of money. How much did each boy have at first?

Thanks!

Hi - I think I can help with Q2.

25/100 = 1/4 of the books were non-fiction.
So, 3/4 of the books were fiction.

7/10 of non-fiction books were borrowed = 7/10 x 1/4 = 7/40
3/10 of fiction books were borrowed = 3/10 x 3/4 = 9/40

7u+9u = 16u
16u = 1600
1u = 1600/16 = 100
Total number of books at the library = 40u = 40 x 100 = 4000

1/4 of 4000 = 1000 non-fiction books
3/4 of 4000 = 3000 fiction books
There were 3000 - 1000 = 2000 more fiction than non fiction books in the library at first.

[kiasuaunt]

1. Hi - Not so sure about this speed Q:


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

2. There are 2 bags of jelly beans labelled A and B. In bag A, there are 470 red jelly beans and 480 green jelly beans. In bag B, there are 350 red jelly beans and 200 green jelly beans. Some red and green jelly beans from bag B are transferred to bag A. As a result, 60 percent of the jelly beans in bag A and 20 percent of those in bag B are red. How many red and how many green jelly beans are transferred from bag B to bag A?

3. There were 544 brownies and cupcakes for sale at a bakery. All the brownies at a bakery cost $488 more than all the cupcakes. After 4/5 of the brownies and 1/4 of the cupcakes were sold, there were twice as many brownies as cupcakes left. Each brownie cost 80 cents less than each cupcake. How much did each brownie cost ?

Thank you.

[tianzhu]

kiasuaunt:

1. Hi - Not so sure about this speed Q:

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

Hi

Good Morning.

It’s helpful to start with a simple diagram for Speed questions.

A common multiple of 7 and 8 is 56.

In 1 h , Mr Lee covered 8 units (56/7)

In 1 h , Mr Wong covered 7 units

In 3 h

Mr Lee ------ 24 units
Mr Wong ------ 21 units

56 – 24 - 21 ------ 11

11 units ------- 110

1 unit ------ 10

8 units -------- 80

Mr Lee’s speed ------- 80 km/h

Best wishes

[tianzhu]

kiasuaunt:

2. There are 2 bags of jelly beans labelled A and B. In bag A, there are 470 red jelly beans and 480 green jelly beans. In bag B, there are 350 red jelly beans and 200 green jelly beans. Some red and green jelly beans from bag B are transferred to bag A. As a result, 60 percent of the jelly beans in bag A and 20 percent of those in bag B are red. How many red and how many green jelly beans are transferred from bag B to bag A?

Hi

This question touches on SE.

You may use MD, UP or use letters of the alphabet to show the variables.

Due to time constraints, I’ll just provide some pointers using UP.

At first

Bag A

R:G ------ 470:480

Bag B

R:G ------ 350:200

After the transfer

Bag A

R:G ------ 3u:2u

Bag B

R:G ------ 1p:4p

3u + 1p ------- 820 (470 + 350)

2u + 4p ------ 680 (480 + 200)

12u + 4p ------ 3280

10u ------ 2600

1u ------ 260

Bag A

R:G ------ 3u:2u ------- 780:520

Red ----- 780 – 470 ------ 310

Green ----- 520 - 480 ------ 40

Best wishes