Q&A - PSLE Math

[Cheerfuldad]

Hi PiggyLalala,


Thank you for your answer!

God bless!

PiggyLalala:

Cheerfuldad:

Hi all,

Need your help!

Q1. Michelle had 60% more cards than Adila. Usha had 35% fewer cards than Michelle. Michelle and Adila gave Usha some cards in the ratio of 3:1. As a result, Usha had 1 1/2 times as many cards as before. Given that Michelle had 238 more cards than Adila in the end, how many cards did Michelle give to Usha?

TIA

This is how my ds will do such a question. I would like to know the model method though.

Michelle: Adila = 160:100 = 8:5 = 40:25
Usha: Michelle = 65:100 = 13:20 = 26:40
Therefore M:A:U = 40:25:26
Let M:A:U = 40p:25p:26p
At the end: M: 40-3u; A: 25p - u; U: 3/2 x 26p = 39p
( M gave 3u cards to U and A gave u cards to U. U got 4u cards from M and U)

Therefore 4u = 39p - 26p = 13p ------ (1)
40p - 3u = 25p - u + 238
15p = 2u + 238
30p = 4u + 476
30p = 13p + 476 from (1)
17p = 476
p = 476/17 = 28.
4u = 13p = 13 x 28 = 364
u = 91
3u = 273
Therefore M gave 273 cards to U.

[smileplease]

Please help :


Colin had $80 more than Donovan at first. After Colin spent 75% of his money and Donovan spent 40% of his money, Donovan had $50 more than Colin. How much money did Colin have at first?

:thankyou:

[tianzhu]

kavisuresh:

6.Mrs.Tan had 130 durians and mangosteens. After she sold 2/3 of the durians and 2/5 of the mangosteens , she had 36 more mangosteens than durians left. How many fruits had he left in all ?

Hi

This question was discussed in one of the earlier posts.

Best wishes

http://farm5.static.flickr.com/4105/5038442191_d4e1a30910_z.jpg\">

[tianzhu]

kavisuresh:

7. Ahmad and Halim together took 5 days to paint the house. If Ahmad and Halim work together for 2 days, followed by Ahmad working alond for 8 days, Halim will take 1 more day to complete the remaining work.How long will Ahmad take to paint the house all by himself ?

Hi

This question touches on “Rates”.

There is more than one way to solve it.

One possible solution is:

When Ahamd and Halim work together, they can paint their house in 5 days.
In 1 day, they can paint 1/5 of their house or 1 unit.

Hence, 1 day of Ahmad + 1 day of Halim ----- 1 unit

In 2 days, they can paint 2/5(2 units) of their house, this means 3/5(3 units) of their house is left unpainted.

8 days of Ahmad + 1 day of Halim ----- 3 units
1 day of Ahmad + 1 day of Halim ----- 1 unit

Therefore, 7 days of Ahmad ----- 2 units
17.5 days ----- 5 units(whole house)

Ahmad took 17.5 days to paint the house all by himself.

Best wishes

[tianzhu]

Cheerfuldad:

Hi all,


Please help with the following questions. (Sorry do not know how to draw the pictures)

Q1. Two rectangular tanks A and B measures 40cm by 20cm by 40cm (height) and 50cm by 40cm by 45cm (height) respectively, Water is being filled by Tap P and Q at a rate of 1.2 litres/min and 5 litres/min in Tank A and Tank B respectively.
At 8 am, Tap P was turned on first.
a) What is the height of the water level in Tank A after 10 minutes?
b) At 8.10 am, Tap Q was then turned on. At what time will the height of the water level in both tanks equal?

Q2. There are 2 overlapping rectangles A and B. The area of rectangle B is 20% more than the area of rectangle A. The unshaded area of rectangle A is 80% of the unshaded area of rectangle B. What percentage of rectangle B is shaded?

Thank you.

Hi

Please refer to Vanilla cake's reply on page 429.

Are those the same questions?

Best wishes

http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&start=4280

[tianzhu]

kavisuresh:

9. A bullet took 5hrs to travel from Patient town to Honest town while an electric train took 4hrs longer to travel from Honest town to Patient town. Both trains set off at the same time and moved towards each other. 2hrs later, they were 255km apart. what was the speed of the electric train ?

Hi

As in any speed question, I suggest you draw a line diagram.

For bullet train, it took 5 hours to cover the journey.
In 1 hour, it travelled 1/5 of the journey

For electric train, it took 9 hours to cover the journey.
In 1 hour, it travelled 1/9 of the journey

In 2 hours time, the two trains covered (2/5 + 2/9) or 28/45 of the journey

45-28 --- 17
17 units --- 255
1 unit --- 15 km

Total journey --- 45U --- 45 x 15 ---675 km

The speed of electric train --- Distance/Time --- 675 / 9 --- 75 km/h

Best wishes

[raghupavithra]

how solve this Express $1 as a percentage of 25-cents.


400%
25%
20%
4%

[Vanilla Cake]

kavisuresh:

2. Alan completed a race in 1h 40min. In the race, he ran at an avg speed of 30m/min from pt A to pt B and then ran back from pt B to pt A at an avg speed of 20m/min. How long did he take to run back to pt A from pt B ?

Constant distance
Ratio of speed
A to B : B to A
30 : 20
3 : 2

Ratio of time
A to B : B to A
2 : 3

Total time taken = 1 h 40 min = 100 min
2u+3u = 5u
5u -> 100 min
Time taken for running from B to A = 3u = 100/5x3= 60 min

kavisuresh:

5.Mdm Ang bought some highlighters, pens and mechanical pencils . 1/4 of them were highlighters. The number of pens she bought was 6 more than 1/2 the total number of all the items and the remaining were mechanical pencils. Each of the highlighters, pens and mechanical pencils cost @2.10, $4.05 and $1.60 respectively. She spent a total of $227.10 on all the items. How many items did she buy altogether ?

Refer to http://4.bp.blogspot.com/_NGNaLTzN5_U/SrxEa7u6fKI/AAAAAAAAD18/ogX5J0DWc5Q/s1600-h/Maths0609SA2P2NYFractionQ18A.JPG and http://www.1800-teacher.com/images/fbfiles/images/P6_160910.jpg.

[Vanilla Cake]

kavisuresh:

4. Given that p: (q+r)= 1:3, r: (q+s)=1:2, p:s = 2:5, a) find p:q:r:s b)find (r+q): (p+s)

Refer to http://4.bp.blogspot.com/_NGNaLTzN5_U/SrxCC0Mik4I/AAAAAAAAD0U/JUyLNBpK1lM/s1600-h/Maths0609SA2P2NYRatioQ12A.JPG and http://www.1800-teacher.com/images/fbfiles/images/P6_160910_Ratio.jpg.

kavisuresh:

8. Tracy counted the number of 10c coins, 20c coins and 50c coins in her piggy bank.The number of 10c coins was 24 more than the number of 50c coins. After spending 3/5 of the 10c coins, 1/4 of 20c coins and 18 50c coins,she had an equal number of 10c and 20c coins. The number of 50c coins now formed 40% of the remaining number of coins. a)How many 10c coins did Tracy have at first ?
b)How much did she spend in all ?

Refer to http://www.onsponge.com/index.php?option=com_kunena&Itemid=282&func=view&id=12598&catid=35#12598.

kavisuresh:

10. At carpark P, the number of lorries to that of vans was in the ratio 3:7. At carpark Q, the number of lorries to that of vans was in the ratio 8:9. When 40% more lorries from an industrial park entered carpark P and 20% of vans at carpark Q moved to carpark P, there were 76 fewer lorries at carpark P than at carpark Q. How many total vehicles were there altogether finally ?

Refer to http://www.onsponge.com/forum/35-thinkingmathonsponge/950-real-hard-ratio.html.

[Vanilla Cake]

kavisuresh:

1. The average mass of some parcels in a box was 20kg at first. When another parcel which weighs 10kg is added to the box, the average mass becomes 18kg. How many parcels are in the box now ?

Refer to http://www.onsponge.com/index.php?option=com_kunena&Itemid=282&func=view&id=11322&catid=35#11322 and you should be able to work out the answer as 5 parcels are in the box now.

kavisuresh:

3. At an enrichment camp, the number of boys was 45% of the number of girls. When 20% of the boys left the camp, there were 192 more girls than boys. How many children were at the camp at first ?

Before
B : G
45 : 100
9 : 20

After
7.2 : 20

20u-7.2u=12.8u = 192
u = 15

At first, number of children at the camp = 9u+20u = 29u = 29x15 = 435.