For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
1)
On a train, the ratio of the number of adults to the number of children is 3:7. After 21 children and 21 adults boarded the train, there are now twice as many children as adults. How many adults were there on the train at first
Answer:_______________
2)
On a cruise, the ratio of the number of boys to the number of girls is 1:5. After 24 girls and 24 boys boarded the cruise, there are now twice as many girls as boys. How many boys were there on the cruise at first
Answer:_______________
3)
On a bus, the ratio of the number of males to the number of females is 2:6. After 8 females and 8 males boarded the bus, there are now twice as many females as males. How many males were there on the bus at first
Answer:_______________
4)
On a bus, the ratio of the number of adults to the number of children is 2:5. After 9 children and 9 adults boarded the bus, there are now twice as many children as adults. How many adults were there on the bus at first
Answer:_______________
5)
On a train, the ratio of the number of males to the number of females is 1:4. After 10 females and 10 males boarded the train, there are now twice as many females as males. How many males were there on the train at first
Answer:_______________
6)
On a train, the ratio of the number of adults to the number of children is 3:7. After 16 children and 16 adults boarded the train, there are now twice as many children as adults. How many adults were there on the train at first
Answer:_______________
7)
On a cruise, the ratio of the number of boys to the number of girls is 1:5. After 18 girls and 18 boys boarded the cruise, there are now twice as many girls as boys. How many boys were there on the cruise at first
Answer:_______________
8)
On a bus, the ratio of the number of males to the number of females is 2:6. After 6 females and 6 males boarded the bus, there are now twice as many females as males. How many males were there on the bus at first
Answer:_______________
9)
On a bus, the ratio of the number of adults to the number of children is 2:5. After 7 children and 7 adults boarded the bus, there are now twice as many children as adults. How many adults were there on the bus at first
Answer:_______________
10)
On a train, the ratio of the number of males to the number of females is 1:4. After 18 females and 18 males boarded the train, there are now twice as many females as males. How many males were there on the train at first
Answer:_______________
1)
On a train, the ratio of the number of adults to the number of children is 3:7. After 21 children and 21 adults boarded the train, there are now twice as many children as adults. How many adults were there on the train at first
Answer: 63
SOLUTION 1 :
Before
Adults
:
Children
:
Difference
3
:
7
:
4
After
Adults
:
Children
:
Difference
1x4
:
2x4
:
1x4
4
:
8
:
4
Step 1:
4 units - 3 units
= 1 unit
1 unit
= 21
Step 2:
3 units
= 3 x 21
= 63
2)
On a cruise, the ratio of the number of boys to the number of girls is 1:5. After 24 girls and 24 boys boarded the cruise, there are now twice as many girls as boys. How many boys were there on the cruise at first
Answer: 8
SOLUTION 1 :
Before
Boys
:
Girls
:
Difference
1
:
5
:
4
After
Boys
:
Girls
:
Difference
1x4
:
2x4
:
1x4
4
:
8
:
4
Step 1:
4 units - 1 unit
= 3 units
Step 2:
3 units
= 24
1 unit
= 24 ÷ 3
= 8
3)
On a bus, the ratio of the number of males to the number of females is 2:6. After 8 females and 8 males boarded the bus, there are now twice as many females as males. How many males were there on the bus at first
Answer: 8
SOLUTION 1 :
Before
Males
:
Females
:
Difference
2
:
6
:
4
After
Males
:
Females
:
Difference
1x4
:
2x4
:
1x4
4
:
8
:
4
Step 1:
4 units - 2 units
= 2 units
2 units
= 8
4)
On a bus, the ratio of the number of adults to the number of children is 2:5. After 9 children and 9 adults boarded the bus, there are now twice as many children as adults. How many adults were there on the bus at first
Answer: 18
SOLUTION 1 :
Before
Adults
:
Children
:
Difference
2
:
5
:
3
After
Adults
:
Children
:
Difference
1x3
:
2x3
:
1x3
3
:
6
:
3
Step 1:
3 units - 2 units
= 1 unit
Step 2:
1 unit
= 9
2 units
= 2 x 9
= 18
5)
On a train, the ratio of the number of males to the number of females is 1:4. After 10 females and 10 males boarded the train, there are now twice as many females as males. How many males were there on the train at first
Answer: 5
SOLUTION 1 :
Before
Males
:
Females
:
Difference
1
:
4
:
3
After
Males
:
Females
:
Difference
1x3
:
2x3
:
1x3
3
:
6
:
3
Step 1:
3 units - 1 unit
= 2 units
Step 2:
2 units
= 10
1 unit
= 10 ÷ 2
= 5
6)
On a train, the ratio of the number of adults to the number of children is 3:7. After 16 children and 16 adults boarded the train, there are now twice as many children as adults. How many adults were there on the train at first
Answer: 48
SOLUTION 1 :
Before
Adults
:
Children
:
Difference
3
:
7
:
4
After
Adults
:
Children
:
Difference
1x4
:
2x4
:
1x4
4
:
8
:
4
Step 1:
4 units - 3 units
= 1 unit
1 unit
= 16
Step 2:
3 units
= 3 x 16
= 48
7)
On a cruise, the ratio of the number of boys to the number of girls is 1:5. After 18 girls and 18 boys boarded the cruise, there are now twice as many girls as boys. How many boys were there on the cruise at first
Answer: 6
SOLUTION 1 :
Before
Boys
:
Girls
:
Difference
1
:
5
:
4
After
Boys
:
Girls
:
Difference
1x4
:
2x4
:
1x4
4
:
8
:
4
Step 1:
4 units - 1 unit
= 3 units
Step 2:
3 units
= 18
1 unit
= 18 ÷ 3
= 6
8)
On a bus, the ratio of the number of males to the number of females is 2:6. After 6 females and 6 males boarded the bus, there are now twice as many females as males. How many males were there on the bus at first
Answer: 6
SOLUTION 1 :
Before
Males
:
Females
:
Difference
2
:
6
:
4
After
Males
:
Females
:
Difference
1x4
:
2x4
:
1x4
4
:
8
:
4
Step 1:
4 units - 2 units
= 2 units
2 units
= 6
9)
On a bus, the ratio of the number of adults to the number of children is 2:5. After 7 children and 7 adults boarded the bus, there are now twice as many children as adults. How many adults were there on the bus at first
Answer: 14
SOLUTION 1 :
Before
Adults
:
Children
:
Difference
2
:
5
:
3
After
Adults
:
Children
:
Difference
1x3
:
2x3
:
1x3
3
:
6
:
3
Step 1:
3 units - 2 units
= 1 unit
Step 2:
1 unit
= 7
2 units
= 2 x 7
= 14
10)
On a train, the ratio of the number of males to the number of females is 1:4. After 18 females and 18 males boarded the train, there are now twice as many females as males. How many males were there on the train at first