1.
A farmer had a twice as many chicken as ducks. After he had sold 200 chickens, he had thrice as
many ducks as chickens. How many chickens did he have at first? Ans.: 240
chicken
ducks
2u x 3
= 6u
1u x 3
= 3u
-200
x
6u – 1u --> 200
5u --> 200
1u --> 200 ÷ 5 = 40
6u --> 6 x 40 = 240 (ans.)
1u
3u
2.
Jane and Ivan had $60. After giving Ivan $8, Jane had the same amount of money as Ivan. How
much money did Ivan have at first? Ans.: $22
-8
Jane
1u
60
60
Ivan
?
+8
2u --> 60
1u --> 60 ÷ 2 = 30
30 - 8 = 22 (ans.)
1u (30)
3.
Thomas is 4 times as old as Sandra. Thomas will be twice as old as Sandra in 8 years time. How
old is Thomas now? Ans.:16
Thomas
Sandra
+8
4u
1u
3u
+8
6u – 4u --> 8
2u --> 8
1u --> 8 ÷ 2 = 4
Thomas (now): 4u --> 4 x 4 = 16 (ans.)
2u x 3 =6u
1u x 3 =3u
1u x3
=3u
4.
John and Ramesh had an equal amount of sweets at first. John bought another 6 sweets and
Ramesh lost 12 of her sweets. John had thrice as many sweets as Ramesh. Find the number of
sweets each of them have first? Ans.:21
3u
John
Ramesh
6
1u
12
3u – 1u --> 12+ 6
2u --> 18
1u --> 18 ÷ 2 = 9
Each (1st): 1u + 12 --> 9 + 12 = 21 (ans.)
5.
Some children were sharing oranges. If each child took 3 oranges, there would be 2 left over.
But if each child took 4 oranges, there would be 2 oranges short. How many oranges were
there? Ans.:14
Total
3 each (12)
2
2
4 each
4 each – 3 each --> 2 + 2
1 each --> 4
3 each --> 3 x 4 = 12
Total:12 + 2 = 14 (ans.)
6.
A moment ago, Wendy had 2/5 as much money as Mike. Wendy withdrew $50 from her bank
account. Now Wendy has 1/2 as much money as Mike.
(a) How much money does Wendy have now? Ans.:$250
(b) What was the total amount of money the two of them had a moment ago? Ans.: $700
Wendy
Mike
2u x 2
= 4u
+50
5u x 2
= 10u
x
1u x 5
= 5u
2u x 5
= 10u
5u – 4u --> 50
1u --> 50
Wendy (now) 5u --> 5 x 50 = 250 (ans.)
Total (Before): 4u +10 u = 14u
14u --> 14 x 50 = 700 (ans.)
7.
Alex and his sister, Amber have a total of 120 computer games. If Alex gives Amber 5 games,
Amber will have nine times as many games as Alex. How many more games does Amber have
than Alex? Ans.: 86
Alex
?
17
-5
1u
120
120
Amber
103
+5
1u + 9u --> 120
10u --> 120
1u --> 120 ÷ 10 = 12
Alex (1st): 1u + 5 = 12 +5 = 17
120 – 17 = 103
103 – 17 = 86 (ans.)
9u
8.
Olivia's mother was 4 times Olivia age 4 years ago. If their total age now is 48, how old is Olivia
now? Ans.:12
4 years ago
48 – 4 – 4
= 40
mother
Olivia
4u
1u
now
+4
+4
4u + 1u --> 40
5u --> 40
1u --> 40 ÷ 5 = 8
Olivia (Now): 1u + 4 = 8 +4 = 12 (ans.)
48
9.
A moment ago, 84 pears and 65 apples were displayed at a fruit stall. 28 pears were sold and
some more apples were displayed. Now, 5 times as many apples as pears are displayed. How
many apples have just been displayed? Ans.:215
A moment ago
pears
apples
84
65
Now
-28
+?
1u --> 84 – 28 = 56
5u --> 5 x 56 = 280
?: 280 – 65 = 215 (ans.)
1u
5u
(280)
10.
Mrs. Tay has a bag of sweets. If she gives each child 7 sweets, she will be left with 5 sweets. If
she gives each child 9 sweets, she will need 5 more sweets.
a)How many children are there? Ans.:5
b)How many sweets are there? Ans.:40
Total
7 each
(35)
5
5
9 each
9 each – 7each --> 5 + 5
2 each --> 10
1 each --> 10 ÷ 2 = 5 (a)
7 each --> 7 x 5 = 35
Total: 35 + 5 = 40 (b)
11.
Jason and Kevin were given some money each. If Jason and Kevin spent $100 and $50 each day
respectively, Jason would have $1300 when Kevin had spent all his money. If Jason and Kevin
spent $50 and $100 each day respectively, Jason would have $3700 when Kevin spent all his
money. How much money was given to Jason in the beginning? Ans.:$4500
Jason
Kevin
100u
1300
-100 u
-50 u
50u
1300
0
75u
Jason
Kevin
100u
50u
1300
-50 p ÷2
-25u
-100 p ÷2
-50u
1300
3700
0
75u --> 3700 – 1300 = 2400
1u --> 2400 ÷ 75 = 32
Jason (1st): 100u + 1300 --> 100 x 32 + 1300 = 4500 (ans.)
12.
Joe has 60% more marbles than Fred. First, Joe gave 20% of his marbles to Fred. In return, Fred
gave 1/6 of his marbles to Joe. Finally, Fred had 80 fewer marbles than Joe. How many marbles
did Joe have at first? Ans.:320
3/5
1/5
Joe
8u x 5 = 40u
-8u
Fred
5u x 5 = 25u
+8u
32u
33u
10u --> 80
1u --> 80 ÷ 10 = 8
40u --> 40 x 8 = 320 (ans.)
+5.5u
-1/6
-5.5u
8/40
37.5u
27.5u
80
10u
13.
When Mr Wong was Meimei's present age, she was 3 years old. When Meimei is Mr Wong's
present age, he will be 81 years old.
a)How much older is Mr Wong than Meimei? Ans.:26
b)How old is Mr Wong now? Ans.:55
Was
Wong
Meimei's
3
3
Present
1u
3
1u
3
Future
2u
1u
81
1u
3
2u
1u
2u + 1u --> 81 - 3
3u --> 78
1u --> 78 ÷ 3 = 26 (a)
Wong (Now): 3 +2u --> 3 + 2 x 26 = 55 (b)
14.
Alex and Betty each had $600 at first. Alex spent $6 per day and Betty spent $2 per day. How
long did it take for Betty's money to be twice as much as Alex's money? Ans.:60 days
Alex
Betty
-6 u
600
600
-2 u
x2 1p --> 600 – 6u
2p --> 1200 – 12u
1p
2p
2p --> 600 – 2u
1200
2p
12u
2p
2u
600
12u – 2u -->1200 – 600
10u --> 600
1u --> 600 ÷ 10 = 60 (ans.)
15.
If Eddie uses his money to buy 7 similar bags, he will have $5 more than Alice. If Alice uses some
of her money to buy same 7 bags, she will have $47 less than Eddie.
a)Find the cost of 1 bag. Ans.:$3
b)How much more money does Eddie have than Alice? Ans.:$26
?
Eddie
7 bags
$5
Alice
7 bags
$47
7 bags + 7 bags --> 47 - 5
14 bags --> 42
1 bag --> 42 ÷ 14 = 3 (a)
7 bags --> 7 x 3 = 21
21 + 5 = 26 (b)
16.
Mr Tan had some apples and oranges in the ratio 4:5. After selling 170 apples and 25% of the
oranges, the ratio of the apples to oranges left became 1:2. What was the number of fruits Mr
Tan had in the end ? Ans.:450
1/4
5/20
apples
oranges
4u x 4 = 16u
5u x 4 = 20u
-170
1p x 7.5 = 7.5u
-5u
16u – 7.5u --> 170
8.5u --> 170
1u --> 170 ÷ 8.5 = 20
Total (end): 7.5u 15u = 22.5u
+2.5u --> 22.5 x 20 = 450 (ans.)
2
15u
2p x 7.5 = 15u
17.
Box A contained 350 black marbles and 500 white marbles. Box B contained 400 black marbles
and 100 white marbles. After some black and white marbles were removed from Box B to be
placed in Box A, 1/2 of the marbles in Box A were black and 3/4 of the marbles in Box B were
black.
a)How many black marbles were removed from Box B to be placed in Box A? Ans.:175
b)How many white marbles were removed from Box B to be placed in Box A? Ans.:25
Box A
black
white
+?
350
Box B
-?
1u
+?
500
1u
1u + 1p --> 500 + 100
1u + 1p --> 600
1u --> 600 – 1p
1u + 3p --> 350 + 400
1u + 3p --> 750
1u --> 750 – 3p
750
1u
1u
600
3p
1p
3p – 1p --> 750 - 600
2p --> 150
400
100
-?
(225)
3p
1p
(75)
1p --> 150 ÷ 2 = 75
3p --> 3 x 75 = 225
400 - 225 = 175 (a)
100 - 75 = 25 (b)
18.
When Kok's age was twice as Bala's age, Mike's age was 30. When Mike's age was twice Kok's
age, Bala's age was 21. Given that Mike was the oldest among the three persons, find Bala's age
when Mike was 62 years old. Ans.:35
Mike‘s
Kok‘s
Bala‘s
2p
30
2u
1u
1u
1u
1p
1p
21
21
2u + 1u --> 30 - 21
3u --> 9
1u --> 9 ÷ 3 = 3
62
(1u + 21)
1u
?
2u + 21 --> 2 x 3 + 21 = 27
62 – 27 = 35 (ans.)
2u + 21
(27)
19.
Jane and Iris has 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25%
as many sweets as Iris. She was left with twice as many sweets as Iris.
a)How many sweets did Iris give away? Ans.:60
1/4
b)How many sweets did Jane have in the end? Ans.:120
Jane
255
Iris
-1u
135
15
120
-4u
2p
1p
Iris: (255 – 15) ÷ 2 = 120
Jane: 120 + 15 = 135
2p --> 135 – 1u x2 1p --> 120 – 4u
2p --> 240 – 8u
240
2p
2p
135
8u
1u
8u – 1u --> 240 - 135
7u --> 105
1u --> 105 ÷ 7 = 15
Iris (gave): 4u --> 4 x 15 = 60 (a)
Jane (end): 135 – 1u --> 135 – 15 = 120 (b)
20.
If I buy 3 Oranges and 5 Apples, I will have $0.70 left. If I buy 4 oranges and 4 apples, I will need
another $0.50. Given that an apple costs $0.80, find the amount of money I have. Ans.:$10.70
$4
$3.20
Total
3 OR
$4
4 OR
$0.70
$0.50
$3.20
4 OR – 3 OR --> 4 + 0.70 + 0.50 – 3.20
1OR --> 2
Total: 3 OR + 4 + 0.70 --> 3 x 2 + 4.70 = $10.70 (ans.)
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