1. Simplify the following ratios.
(a) 10  20
(b) 5  15
(c) 18  12
(d) 40  24
2. Simplify the following ratios.
1 1

2 4
(d) 800 g  0.5 kg
(a) 0.2  0.6
(b)
(c) 20 cm  1 m
3. Each of the following is formed by identical figures. Find the ratio of the area of the shaded regions to
that of the unshaded regions.
(a)
(b)
(c)
4. (a) If 1 : 2  x : 4, find the value of x.
(b) If 3 : 4  12 : y, find the value of y.
(c) If z : 10  9 : 5, find the value of z.
5. There are 12 pieces of salmon sushi and 20 pieces of California rolls in a package. Find the ratio of the
number of salmon sushi to that of California rolls.
6. There are 42 students in S1B where 20 of them wear glasses.
(a) Find the ratio of the number of students wearing glasses to that of the whole class.
(b) Find the ratio of the number of students without wearing glasses to that of the whole class.
(c) Find the ratio of the number of students wearing glasses t o those without wearing them.
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7. Mother divides 28 candies in the ratio of 4 : 3 and gives them to her daughter and son respectively. How
many candies does each of her daughter and son get?
8. (a) If 10 : 6  (x  1) : 3, find the value of x.
(b) If 9 : 2  18 : (y  3), find the value of y.
(c) If (z  5) : 4  7 : 2, find the value of z.
9. In the following, x, y, a, b, h and k are non-zero.
(a) If 3x  4y, find x : y.
a b
(b) If  , find a : b.
2 3
(c) If h is 0.6 time of k, find h : k.
10. There are altogether 30 $2 and $1 coins in a bag. If the ratio of the number of $2 coins to that of
$1 coins is 5 : 1,
(a) what is the total value of $2 coins in the bag?
(b) what is the total value of $1 coins in the bag?
(c) find the ratio of the total value of $1 coins to that of all coins in the bag.
11. Simplify the following ratios.
(a) 4 : 8 : 12
(b) 14 : 7 : 42
(c) 18 : 30 : 12
(b) x : y  1 : 2, y : z  2 : 5
(c) x : y  9 : 4, y : z  4 : 3
12. Find x : y : z for each of the following.
(a) x : y  2 : 1, y : z  1 : 10
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13. Find x : y : z for each of the following.
(a) x : y  5 : 3, x : z  5 : 4
(b) y : x  3 : 2, y : z  9 : 7
(c) x : z  3 : 2, y : z  1 : 6
14. It is given that a, b and c are non-zero. Find a : b : c for each of the following.
a
b 1
a 1
(a)
(b)
(c) 4a  5b  2c
 1, 
 , b  3c
b 2
b
c 2
15. There are 45 gold coins, 60 silver coins and 90 copper coins in a bag. Find the ratio of the number of
gold coins, silver coins and copper coins in the bag.
16. Cindy has 6 English books, 10 Chinese books and 2 Japanese books.
(a) Find the ratio of the number of English books, Chinese books and Japanese books.
(b) If Cindy buys 2 English books, 2 Chinese books and 4 Japanese books, find the ratio of the number
of English books, Chinese books and Japanese books owned by Cindy now.
17. Keith divided $6 000 in the ratio of 3 : 2 : 1. Find the amount of the largest portion.
18. There are altogether 30 apples, mangoes and pears in a basket. The number of apples and mangoes are in
the ratio of 3 : 2. The number of mangoes and pears are in the ratio of 4 : 5.
(a) Find the ratio of the number of apples, mangoes and pears.
(b) Find the number of pears.
19. Copper, zinc and gold are melted together into an alloy in the ratio of the weight of 3 : 2 : 4. The weight
of copper is 72 g. Find the weight of the alloy.
5
20. The monthly salary of Gibson is 3 times that of Dicky. The monthly salary of Cathy is
of that of
2
Dicky.
(a) Find the ratio of the monthly salaries of Gibson, Cathy and Dicky.
(b) If the total monthly salary of them is $34 060, what is the monthly salary of each of them?
12.15
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21. Match items in column A to those in column B.
Column A
Column B
(a)
5 km/h


(i)
(b)
$5/unit


(ii) $5 per square metre
(c)
$5/m2


(iii) $5 per unit
(d)
5 m/s


(iv) $5 per metre
(e)
$5/dozen


(v) 5 kilometres per hour
(f)
$5/m


(vi) 5 metres per second
$5 per dozen
22. Complete the following table.
Distance
Time
Speed
(a)
5 km
1h
km/h
(b)
250 km
5h
km/h
(c)
20 m
5s
m/s
(d)
125 m
20 s
m/s
23. 5 bottles of 1.5 L apple juice are sold at $45. Find the price of the apple juice
(a) in $/bottle.
(b) in $/L.
24. A car travelled 144 km in 2 hours. Find the speed of the car
(a) in km/h.
(b) in m/s.
25. The price of lemon tea in a pack of 9 is $19.8. The price of lemon tea in a pack of 6 is $14.4.
(a) Find the price of lemon tea in a pack of 9 in $/carton.
(b) Find the price of lemon tea in a pack of 6 in $/carton.
(c) Which pack of lemon tea is more economical?
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26. Suki typed 540 words in 15 minutes. Carmen typed 2 700 words in 1.5 hours.
(a) Find the typing speeds of each of them in words/min.
(b) Who has a higher typing speed?
27. The weekly drawing tutorial fee of Louise is $420.
(a) If there are 3 lessons a week, find the drawing tutorial fee in $/lesson.
(b) If there are 14 lessons in July, find the drawing tutorial fee of Louise in that month.
28. A bus travelled 60 km in 1.5 hours.
(a) Find the speed of the bus in km/h.
(b) If the speed of the bus remains unchanged, find the time required for the bus to trav el 100 km.
29. Suppose we can exchange 5 UK pounds for 76 HK dollars and 4 Canadian dollars for 30.6 HK dollars.
(a) How many HK dollars can we exchange for 100 UK pounds?
(b) How many HK dollars can we exchange for 100 Canadian dollars?
(c) Which currency, UK pounds or Canadian dollars, has a higher exchange rate to HK dollars?
30. Express the following map scales in the form of 1 : n.
(a) 5 cm to 10 m
(b) 20 mm to 4 000 cm
(c) 60 cm to 12 km
31. For the road of 10 km long, its length on the map is 5 cm. Find the scale of the map in the form of
1 cm : n km.
32. It is given that the scale of a map is 1 cm to 200 m. If the actual distance between a playground and a
library is 700 m, find the distance between them on the map.
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33. It is given that the scale of a drawing is 1 cm : 42 m. If the height of a building in the drawing is 3.5 cm,
find the actual height of the building.
Height
Scale drawing: 1 cm : 42 m
34. It is given that the scale of a map is 1 : 10 000. For two buildings which are 800 m apart, find the
distance between them on the map.
35. On a map, the distance between city A and city B is 8 cm. If the scale of the map is 1 : 1 000 000, find
the actual distance between the two cities.
36. On a floor plan with a scale of 1 : 200, the length and width of a room are 3 cm and 4 cm respectively.
(a) Find the actual dimensions of the room. (Give your answer in length  width.)
(b) Find the actual area of the room in m2 .
37. The figure shows the floor plan of a flat with a scale of 1 : 200.
1.7 cm
1 cm
Bathroom
1.5 cm
1.15 cm 1.15 cm
1 cm
Store room
1.5 cm
0.5 cm
Sitting room
2 cm
Master bedroom
Bedroom
1.5 cm
6.5 cm
Scale: 1 : 200
(a) Find the actual area of the store room in m2 .
(b) Find the actual area of the master bedroom in m2 .
12.18
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3.5 cm
Kitchen