Hello everyone, I received an email from a reader seeking some help. Below is the email reproduced unedited. Please feel free to help.
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Hi,
I am a regular reader of your blog "road-to-psle". I have 1 question from CHIJ St Nicholas 2009 Prelim Paper 2 Q17 that I cannot solve. I have asked many people including tutors and teachers but they also cannot solve. Can you please help me? The question:
At Carpark P. the number of lorries to that of vans was in the ralio 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 the vans at Carpark Q moved to Carpark P. there were 76 fewer
Iorries at Carpark P than at Carpark Q. How many vehicles were there
altogether at the two carparks finally? Ans:564
Thanks
John
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Please post solutions here.
http://www.atfreeforum.com/excel/viewtopic.php?p=5&mforum=excel#5
Tuesday, June 22, 2010
Request for help - CHIJ St Nicholas 2009 Prelim Paper 2 Q17
Saturday, May 01, 2010
Time for a Breather
While it is good to be consistently studying, there must also be short break periods to relax. Here are two video clips for you to enjoy.
Johann Pachelbel's Canon in D (rock violin - duet)
(rock violin - solo)
Wednesday, April 14, 2010
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q18
Sparkles Jewellery Shop sold diamonds, rubies and emeralds. 3/5 of the gemstones were diamonds. There were 168 fewer rubies than diamonds. The ratio of the number of rubies to the number of emeralds was 7:3. After some rubies were sold, 30% of the remaining gemstones in the shop were rubies and emeralds.
a) How many rubies were sold?
b) Find the percentage decrease in the number of gemstones. Leave your answer as a fraction.
Solution
Rubies --> 7/10 of 2/5 = 14/50
Diamonds - Rubies --> 168 (more diamonds than rubies)
3/5 - 14/50 = 168
16/50 --> 168
1/50 --> 168 divided by 16 = 10.5
Rubies + Emeralds (2/5 of whole)
20/50 --> 20 x 10.5 = 210
2/5 of whole --> 210
1/5 of whole --> 210 divided by 2 = 105
(Diamonds) 3/5 of whole --> 3 x 105 = 315
After selling, Rubies and Emeralds make up 30%, while Diamonds make up 70%.
Diamonds 70% --> 315
10% --> 315 divided by 7 = 45
Rubies and Emeralds 30% --> 3 x 45 = 135
(a)
(Rubies and Emeralds before selling) - (Rubies and Emeralds after selling)
--> 210 - 135 = 75
Answer: 75 rubies
(b)
Percentage decrease in number of gemstones
1/50 of gemstones --> 10.5
50/50 of gemstones -> 50 x 10.5 = 525
75 rubies sold
--> (75/525) x 100% = 14 and 2/7 %
Answer: 14 and two-sevenths %
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q17
The number of boys to the number of girls in Happy Kindergarten was 3:5. The number of boys to the number of girls in Merry Kindergarten was 4:5. Both kindergartens had the same number of boys. When 10 girls from Happy Kindergarten joined Merry Kinderten, the ratio of the number of boys to the number of girls in Happy Kindergarten became 2:3. Find the total enrolment of the 2 kindergartens.
Solution
Happy
B : G
3 : 5
(multiply both by 4)*
12 : 20
(Total units --> 12 + 20 = 32)
Merry
B : G
4 : 5
(multiply both by 3)*
12 : 15
(Total units --> 12 + 15 = 27)
* Happy (x4) and Merry (x3) to make the number of units for boys in both kindergartens the same, because the number of boys are the same for both kindergartens.
After 10 girls left Happy to join Merry,
Ratio in Happy
B : G
2 : 3
(multiply by 6)**
12 : 18
** (x6) to make units for boys 12 again.
Number of units for girls in Happy before transfer --> 20 units
Number of units for girls in Happy after transfer --> 18
20 units - 18 units --> 10
2 units --> 10
1 unit --> 10 divided by 2 = 5
Total for enrolment for both kindergartens
Happy --> 32 units
Merry --> 27 units
32 units + 27 units --> 59 units
59 units --> 59 x 5 = 295
Answer: 295 children
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q16
Ali and Minhua were playing a card game using 96 cards. In the first game, Minghua lost 1/5 of his cards to Ali. In the second game, Ali lost 1/3 of his cards to Minghua. After the second game, both boys had the same number of cards. How many cards did Ali have at first?
Solution
Before 1st game
Minghua --> 5 units
Ali --> 11 units
Total 16 units --> 96
1 unit --> 96 divided by 16 = 6
11 units --> 66
Answer: 66 cards
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q15
There were some prizes ot be won at a Shop and Win Contest. 35% were cash prizes and there rest were household items. Some cash prizes were given out and the percentage of cash prizes decreased to 22%. If there were 54 more household items than cash prizes at first, find the number of cash prizes being removed.
Solution
Before
Cash --> 35%
Household Items consists of
--> 35% + 30%(54 items) = 65%
30% --> 54
1% --> 54 divided by 30 = 1.8
(Cash before) 35% --> 35 x 1.8 = 63
(Household Items) 65% --> 65 x 1.8 = 117
After
Cash became --> 22%
Household Items --> (remaining) 78%
78% --> 117
1% --> 117 divided by 78 = 1.5
(Cash after) 22% --> 22 x 1.5 = 33
Cash before - Cash after --> Cash prizes removed
63 - 33 = 30
Answer: 30 cash prizes
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q14
There were ducks, goats and hens at a farm. 15% of the animals were ducks. There were 180 fewer ducks than hens. The remaining 121 animals were goats. What percentage of the animals at the farm were goats? Levae your answer correct to 2 decimal places.
Solution
* 180 more hens than ducks, therefore hens --> 15% + 180.
** Ducks (15%) and hens (15% + 180), therefore goats give the remaining 70% less 180.
70% - 180 --> 121
70% --> 121 + 180 = 301
10% --> 301 divided by 7 = 43
100% 10 x 43 = 430
Percentage of animals were goats
--> (121/430) x 100% = 28.139% ~ 28.14%
Answer: 28.14%
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CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q13
Abbie, Ellen and Faheem sold umbrellas to raise funds for charity. Each umberlla was priced at $22.50. Abbie sold 1/6 of the umbrellas while Ellen and Faheem sold the remaining umbrellas in the ratio of 2:7 respectively. If Faheem sold 364 umbrellas more than Abbie, what was the total amount of money collected by them?
Solution
Abbie --> 1/6
Remaining --> 5/6
Since ratio for Ellen : Faheem is 2 : 7,
Faheem sold 7/9 of remainder
Faheem (7/9 of the remaning 5/6)
--> 7/9 x 5/6 = 35/54
(Faheem - Abbie) --> 35/54 - 1/6 = 13/27
13/27 --> 364 (Faheem sold 364 more than Abbie)
1/27 --> 364 divided by 13 = 28
27/27 --> 27 x 28 = 756
756 x $22.50 = $17 010
Answer: $17 010
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q12
The figure below is made up of 2 squares and a rectangle. The ratio of the area of A to the area of B to the area of C is 9:4:3. The ratio of the unshaded part of B to the unshaded part of C is 4:1. If the shaded part is 56 square cm, find the area of A that is not covered by B.
Solution
(C) 3 parts --> 56 sq cm + 1 unit
(multiply by 4)
(C) 12 parts --> 224 sq cm + 4 units
(B) 4 parts --> 56 sq cm + 4 units
12 parts - 4 parts --> 224 sq cm - 56 sq cm
8 parts --> 168 sq cm
1 part --> 168 sq cm divided by 8 = 21 sq cm
(A - B) 5 parts --> 5 x 21 sq cm = 105 sq cm
Answer: 105 square cm
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q11
Jai, Maira and Lynn have 760 stickers altogether. Jai has 8/9 as many stickers as Maira and 6/11 as many stickers as Lynn. If Jai and Lynn want to have an equal number of stickers, how many stickers must Lynn give to Jai?
Solution
(48 + 54 + 88) units --> 760 stickers
190 units --> 760
1 unit --> 760 divided by 190 = 4
Lynn must give Jai 20 units for Lynn and Jai to have equal number of stickers.
20 units --> 20 x 4 = 80
Answer: 80 stickers
