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The ratio of boys to girls in Mr. Brown’s math class is 2 : 3. If there are 30 students in the
class, how many more girls than boys are in the class?
2. Half the people in a room left. One third of those remaining started to dance. There were
then 12 people who were not dancing. The original number of people in the room was
3. Last summer 100 students attended basketball camp. Of those attending, 52 were boys and
48 were girls. Also, 40 students were from Jonas Middle School and 60 were from Clay Middle
School. Twenty of the girls were from Jonas Middle School. How many of the boys were from
Clay Middle School?
4. Students from three middle schools worked on a summer project.
*Seven students from Allen school worked for 3 days. *Four students from Balboa school
worked for 5 days. *Five students from Carver school worked for 9 days.
The total amount paid for the students’ work was $774. Assuming each student received the
same amount for a day’s work, how much did the students from Balboa school earn altogether?
5. 444 teachers, boys and girls joined a school camp. The ratio is 1:6:5 respectively. How many
groups can be formed if each group must have the same number of teachers, boys and girls as
the other groups?
6. Linda has 2 containers, Container A and Container B. The amount of water in Container A
is ⅘ of the amount in Container B at first. When 200 ml of water from Container A is poured
into Container B, the amount of water in Container A is ½ the amount in Container B. How much water was in Container A at first?
7. At first, John had 20 books while Lindy had 25 books. After Lindy gave John some books,
the ratio of the number of books John had to that of Lindy was 7:2. How many books did
Lindy give to John?
8. The number of books Pei Pei has is ⅔
the number of books that Lin Lin has. If Lin Lin gives
Pei Pei 4 books, then Pei Pei and Lin Lin will have an equal number of books. How many
books does Pei Pei and Lin Lin have altogether?
9. The ratio of the number of students from class 5A to that of class 5B was 5:4 at first. After 8
students from class 5A were transferred to class 5B, the ratio became 3:4. How many students
were there in class 5A before the transfer?
10. Alice is reading a story book. The ratio between the number of pages she has read and the
number of pages she has not read is 1 : 5. If she reads 20 pages more, then the new ratio will
be 3 : 5. How many pages are there in the story book?
11. Alice and John had some sweets in the ratio 5:7. After Alice gave John some sweets, the ratio
of the number of sweets Alice had to that of John was 17:31. Express the number of sweets
that Alice gave John as a percentage of the number of sweets she had at first. If your answer
is m%, shade “m” as your answer. For example, if the answer is 50%, shade “50”.
12. A painter mixed different colour of paint in a pail. He mixed 8 litres of blue paint and 12 litres
of yellow paint together in the pail to obtain green paint. Not satisfied with the colour of the
mixture, he poured away 5 litres of the mixture and added blue paint to obtain the original
volume. What percentage of the final mixture was made up of blue paint?
13. Mimi was making an Orange syrup drink. She mixed 1 litre of the Orange syrup with 4 litres of
water in a container. Her mother tried the syrup, found it two sweet and poured away 2 litres
of the mixture. Then she added 2 litres of water to the remaining mixture in the container.
What percentage of the final mixture was made up of water?
14. At first, the ratio of Abel’s savings to Bell’s savings was 7:5. After each of them received $12
from their parent, the ratio of Abel’s savings to Bell’s savings became 5:4. What was Bell’s
savings (in $) at first?
15. There are some black marbles and white marbles in a box. At first, the ratio of the number of
black marbles to the number of white marbles was 6:7. After 50 black marbles and 25 white
marbles were removed from the box, the ratio of the number of black marbles to the number
of white marbles became 14:17. What was the number of white marbles at first?
16. The number of 50-cent coins that Mary has to the number of 20-cent coins is 5:2 After exchanging some 50-cent coins for the 20-cent coins, Mary has the same amount of money as
before, but the ratio of the number of 50-cent coins to the number of 20-cent coins is now
8:5. Find the increase in the number of 20-cent coins as a percentage of the initial number of
20-cent coins.
17. The figure below shows 4 points (A, B, C and D) lying on a line segment. Given that AB/BC =BC/CD = ⅔ and that AD =2014 cm, find the length of AB (in cm).
18. Sand is packed into 3 types of packages – Type A, Type B and Type C. To fill an empty
container, one can EITHER use 2 packets of Type A and 1 packet of Type B, OR use 2
packets of Type B and 1 packet of Type C. If 1 ⅓of packet Type A and 1 ⅓ packet of Type B are used to fill empty container, what fraction of Type C is required? Multiply your answer by 60.
19. A company sells detergent in three different sizes: Small, Medium and Large. The Medium
size costs 50% more than the Small size and contains 20% less than the Large size. The Large
size contains twice as much detergent as the Small size and costs 30% more than the Medium
size. Rank the three sizes, in terms of value-for-money, from the best to worst.
[Let Small = 1, Medium = 2 and Large = 3.
Suppose your answer is Small, Large, Medium (in that order), then shade your answer as
“123”.]
20. In a certain co-curricular activity (CCA), the ratio of the number of upper primary students to
the number of lower primary students is 3:2. If the ratio of the number of upper primary boys
to the number of lower primary girls is 4:5, find the least possible total number of students.
21. In a particular school, the number of pupils in P5 is the same as the number of pupils in P6.
The ratio of the number of boys to the number of girls in P5 is 5:6 and the ratio of the number
of boys to the number of girls in P6 is 1:1. Given that the ratio of the number of boys in P5
to the number of girls in P6 is x :110, find the value of x.
22. Rosanne went to the market to buy rice. There were 3 grades of rice to buy: Grade A, B and
C. Grade B rice cost 150 cents per kilogram while Grade C rice cost 120 cents per kilogram.
Suppose Rosanne used all her money to buy Grade A rice. If she had used all her money to
buy Grade C rice instead, she would have 5 more kilograms of rice. On the other hand, if she
had used all her money to buy Grade B rice instead, she would have 2 more kilograms of rice.
What was the price of 1 kilogram of Grade A rice?
23. Timmy has 3 apples, Tom has 2 apples and Darryl has none. Assume that all the 5 apples
are of the same sizes and of the same qualities. Three of them finished the apples with equal
shares. After that, Darryl paid Tom 40 cents for Tom’s apple. How much should
Darryl pay Timmy for Timmy’s apple?