P5 Maths Worksheets Singapore - Problem Questions
Revision 8
Name : ____________________
Date : _____________
Score : _____________
Write down your correct answer
and show your workings:
1) Michael bought some apples
and gave half of them to Jackson.
Jackson bought some pears and gave half of them to Michael.
Micheael threw away 25 pears that were rotten while Jackson bought for
himself another 20 apples.
After that, the number of pears to apples Michael had were in the ratio
of 1:4
and the number of pears to apples Jackson had were in the ratio of 1:2.
How many pears did Jackson buy?
Ans: ____________________
2) Mary had a total of 260
black and white beads in the ratio 7:6.
After she gave away an equal number of each type of beads, the number of
black and white beads left was in the ratio 7:2.
How many beads did she give away altogether?
Ans: ____________________
3) A seamstress had 69 round
buttons and 105 oval ones.
After
using an equal number of round and oval buttons, the ratio of the number
of round buttons to oval ones was 3:5.
Find the
number of round buttons she used.
Ans: ____________________
4) In a school, the children
are divided into two camps, A and B.
The ratio of the number of children in Camp A to Camp B is 2:3.
All the children in Camp A are boys.
In camp B, the ratio of the number of boys to girls is 1:3.
(i) What fraction of the children in the school are boys?
(ii) If there are 60 more boys in camp A than B, how many girls are there
in the school?
Ans: ____________________
5) A trapezium is divided
into 4 parts.
A and B form half the trapezium.
C and D form the other half.
The areas
of A and B are in the ratio 2:3.
The areas
of C and D are in the ratio 1:2.
(i) What
fraction of the trapezium is part D?
(ii) If
part B is bigger than part A by 12cm square, find the area of the trapezium.
Ans: ____________________
Answers:
1)
Apple
Pear
Michael 1
1 1 1
1 25
Jackson 1
1 1 1 20
1 25
1 25 1 25
4 units + 20 = 2
units + 50
1 unit = 15
2 units / 50 = 30
+ 50
Jack = 80 pears
Or
Pears : Apple (Jackson)
1u + 25 : 2 ( Pears +
25 because Michael threw away 25 )
Since Jackson bought 20
more apples,
New ratio becomes(Jackson)
Pears : Apple
1u + 25 : 4u + 20 (Apple
half = 4u, he bought 20 so Jackson apple = 4u + 20)
We know from the question that
Jackson pear was twice of the number of apples he had
So, Apple is also-> 2u
+ 50
Our equation ->
4u + 20 = 2u + 50
2u = 50 - 20 = 30
1u = 15
Total pears jackson bought (Do
not forget Michael threw 25 away)
-> ( 1u(15) + 25 ) 2 = (15 +
25) 2 = 40 x 2 = 80 (Answer)
Or
Check
At first, Michael bought
120 apples.
Half of the apples were
given to Jackson = 1/2 x 120 = 60 apples
Number of apples left
for Michael = 120 - 60 = 60 apples
Michael received half
of the 80 pears bought by Jackson -> 1/2 x 80 = 40 pears
Michael threw away 25
rotten pears.
Number of pears left for
Michael = 40-25 = 15 pears
In the end, ratio of the
number of pears to the number of apples left for Michael -> 15:60 = 1:4
Check
At first, Jackson bought
80 pears.
Half of the pears were
given to Michael = 1/2 x 80 = 40 pears
Number of pears left for
Jackson = 80 - 40 = 40 pears
Jackson received half
of the 120 apples bought by Michael -> 1/2 x 120 = 60 apples
Jackson bought another
20 apples.
Number of apples left
for Jackson = 60 + 20 = 80 apples
In the end, ratio of the
number of pears to the number of apples left for Jackson -> 40:80 = 1:2
Number of pears that Jackson
bought was 80
2) Use the concept of "same gap/difference" to
solve this.
The difference in the number
of black and white beads = 1/13 x 260 = 20.
Since same number of each
type of beads were given away, the difference will remain the same.
In the end, number of black
: white = 7u : 2u, so 5u = 20 beads
--> 1u = 4 beads.
Total number of beads
in the end = 9u = 180.
So, number of beads given
away = 260 - 180 =80
3) Difference in number of buttons
= number of oval buttons
more than round buttons
= 105 - 69 = 36
In the end, round : oval = 3u
: 5u, difference = 2u = 36
1u = 18
Number of round buttons left
= 3u = 3 x 18 = 54
Number of round buttons used
= 69 - 54 = 15
4) Camp A : Camp B = 2 : 3
Camp B, boys : Camp B,
girls = 1:3 (total 4)
Make the number for Camp
B the same .. lowest common multiple for 3 & 4 = 12
Camp A: Camp B = 2 : 3
= 8u : 12u, Total = 20u
Camp B, boys : Camp B,
girls = 1 : 3 = 3u : 9u (total 12u = Camp B children)
Total number of boys =
8u (camp A) + 3u ( camp B) = 11u
Boys as fraction of total
number of children in school = 11/20
If there are 60 more boys
in Camp A than Camp B, then
8u - 3u = 60, 5u = 60
1u = 12
Number of girls = 9u =
9 x 12 = 108
5) I will assume that Area of (A+B) = 1/2 Area
of trapezium = Area of (C+D)
Then
A: B = 2:3 = 6u : 9u
C: D= 1:2 = 5u : 10u
a) D as fraction of area of trapezium
= 10u/30u = 1/3
b) B-A = 3u = 12 cm2, 1u = 4
cm2
Area
of trapezium = 30u = 30 x 4 cm2 = 120 cm2 |