05 September 2010
Edwin (DeLasalle Primary 6)
Question: 1)
1/5 of the number of chickens that Farmer Wong had is equal to 3/4 of the number of
chickens that Farmer Zhang had.When Farmer Wong sold 150 of his chickens and Farmer
Zhang bought another 160 chickens,the ratio of the number of chickens that Farmer
Wong had to the number of chickens that Farmer Zhang had became 5:3.What was the
total number of chickens that the 2 farmers have at first?
Initial ratio of Farmer Wong's Chickens to Farmer Zhang's Chickens
---> Farmer Wong : Farmer Zhang
15 : 4
When Farmer Wong sold 150 of his chickens and Farmer
Zhang bought another 160 chickens,the ratio of the number of chickens that Farmer
Wong had to the number of chickens that Farmer Zhang had became 5:3.
---> 15 units - 150 : 4 units + 160
5 : 3
---> 3(15units - 150) = 5(4units + 160) [(The initial base amount of both farmers have changed therefore the need to multiply each other base e.g. 1/3 + 1/4 = (1/3 x 4) + (1/4 x 3 ) = 7/12) ]
---> 45 units - 450 = 20units + 800
---> 45units - 20 units = 800 + 450
---> 25units = 1250 chickens
---> 1 unit = 1250 / 25
= 50
Therefore initial ratio ---> 15units : 4 units
15 units ---> 15 x 50 = 750 chickens (Farmer Wong)
4 units ---> 4 x 50 = 200 chickens (Farmer Zhang)
Total no. of chickens they have at 1st = 750 + 200 = 950 (Ans)
Question :
Louis and Edumund left town B at the same time, heading in the opposite
direction. Louis headed for town C while Edmund left for town A . The speed of
Edmund was 12 km/h faster than that of Louis. After 30 min, Louis had completed 2/3
of his journey while Edmund had compeleted 1/4 of his journey. They were also 90km
apart.Calculate the speed of Louis and how far is Edmund from town A when Louis reached
his destination?
Total Speed of Edmund & Louis = Distance / Time
= 90km / 30min
= 180km/h
Louis's speed --> 1 unit
Edmund's speed --> 1 unit + 12km/h
2 units + 12km/h --> 180km/h
2 units --> 180km/h - 12km/h
--> 168km/h
1 unit --> 168km/h ÷ 2
--> 84km/h (Ans)
Louis's speed is 84km/h
In 30 min, Louis travelled = 30min/60min X 84
= 42km
2/3 of Louis's journey = 42km
3/3 of Louis's journey = 3/2 X 42km
= 63km
Time taken for Louis to complete his journey = Distance / Time
= 63km/84km/h
= 3/4 hr
Edmund's speed = 84 + 12 = 96km/h
In 30 min, Edmund travelled = 30min/60min X 96
= 48km
1/4 of Louis's journey = 48km
4/1 of Louis's journey = 4/1 X 48km
= 192km
In 3/4 hr, Edmund travelled --> 3/4 X 96km/h
--> 72km
Edmund's distance from Town A after Louis had reached Town B = 192km - 72km
= 120km (ANS)#
R1, R2 and R3 are three rectangles not drawn to scale. The area of R1 is 25% ofR2,
while the area of R2 is 48% that of R3.
(a) What is the ratio of area R1 to R2 to R3? Express your answer in the simplest form.
Solution
R1 : R2
25% : 100%
1% : 4%
R2 : R3
48% : 100% ÷ 2
12% : 25%
x3 3% : 12% : 25%
3 : 12 : 25 (Ans)
(b) When the area of R1 is increased, its area becomes 60% that of R3.
What is the percentage increase in the area of R1?
60% of R3 = 60/100 x 25
= 15
15 – 3 = 12
12/3 x 100% = 400%
400% increase in the area of R1. (Ans)
StudentName: Dominic
CurrentLevel: Primary 6 (Delasalle Pri)
QuestionType: Maths
Question: Molly ordered some cookies.1/4 of them were chocolate cookies.1/3 were
butter cookies.The rest were lemon cookies.She ordered 80 more lemon than chocolate
cookies.The supplier was unable to deliver 1/4 of the butter cookies Molly
ordered.She was then given 160 lemon cookies in replacement for the butter cookies
not delivered.What fraction of the total number of cookies received by Molly were
butter cookies?
Solution
1 - 1/4 - 1/3 = 5/12(of the cookies are Lemon cookies)
3/12(of the cookies are Chocolate cookies)-->1/4 x 3
4/12(of the cookies are Butter cookies)--> 1/3 x 4
*She ordered 80 more lemon than chocolate cookies.
5/12(Lemon cookies) - 3/12(Chocolate cookies) = 2/12
2 units --> 80
1 unit --> 80 ÷ 2 = 40 cookies
Total number of
chocolate cookies = 3 units x 40 = 120
Butter cookies = 4 units x 40 = 160
Lemon cookies = 5 units x 40 = 200
*The supplier was unable to deliver 1/4 of the butter cookies Molly
ordered.She was then given 160 lemon cookies in replacement for the butter cookies
not delivered.
1/4 x 160 butter cookies = 40
160 - 40 = 120 (only 120 was delivered)
Total no. of Lemon cookies = 160 + 200 = 360
Total no of cookies = 120 + 120 + 360 = 600
*What fraction of the total number of cookies received by Molly were
butter cookies?
Butter cookies/Total no. of cookies = 120/600 = 1/5 # ( Answer)
StudentName: Roy Lim
CurrentLevel: Primary 5 (Yew Tee Pri)
QuestionType: Maths
Question: Melvin had 75 more apples than oranges. After he had sold 4/5 of the
apples and 3/4 of the oranges, he had 285 fruits left.
a)How many apples did he sell?
b)What fraction of the fruits sold were oranges?
a) Apples --> 1 unit + 15 + 1 unit + 15 + 1 unit + 15 + 1 unit + 15 + 1 unit + 15 ( 5 units + 75)
( 1/5) (1/5) (1/5) (1/5) (1/5)
Orange --> 5 units
*4/5 of apples sold --> 1 - 4/5 = 1/5 left ( i.e 1 unit + 15 )
*3/4 of oranges sold--> 1 - 3/4 = 1/4 left ( i.e 1/4 x 5 units)
= 1/4 x 5
= 1 1/4 units
*..he had 285 fruits left.--> 1unit + 15 + 1 1/4 units --> 285
2 1/4 units --> 285 - 15
--> 270
1 unit --> 270 ÷ 2 1/4
--> 270 ÷ 9/4
--> 270 x 4/9
--> 120
Number of apples sold --> 4 units + 60
--> (4 x 120) + 60
--> 480 + 60 = 540 (Ans)
b)Total number of oranges --> 5 units x 120
--> 600
Number of oranges sold --> 3/4 x 600
--> 450
Total number of fruits sold = 540 + 450
= 990
Fraction of fruits sold as oranges = 450 / 990
= 5 / 11 (Ans)
*See attached word document for model drawing diagram. Click Here
|