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)
The ratio of the number of males to the number of females in a factory was 2:3. After 42 females and 42 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer:_______________
2)
The ratio of the number of males to the number of females in an office was 4:5. After 15 females and 15 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer:_______________
3)
The ratio of the number of boys to the number of girls in a class was 3:4. After 66 girls and 66 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer:_______________
4)
The ratio of the number of males to the number of females in a stadium was 3:4. After 122 females and 122 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer:_______________
5)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 29 childs and 29 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer:_______________
6)
The ratio of the number of males to the number of females in a factory was 2:3. After 60 females and 60 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer:_______________
7)
The ratio of the number of males to the number of females in an office was 4:5. After 20 females and 20 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer:_______________
8)
The ratio of the number of boys to the number of girls in a class was 3:4. After 72 girls and 72 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer:_______________
9)
The ratio of the number of males to the number of females in a stadium was 3:4. After 144 females and 144 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer:_______________
10)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 30 childs and 30 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer:_______________
1)
The ratio of the number of males to the number of females in a factory was 2:3. After 42 females and 42 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer: 126
SOLUTION 1 :
Before
Males
:
Females
:
Difference
2
:
3
:
1
After
Males
:
Females
:
Difference
1
:
2
:
1
Step 1:
2 units - 1 unit
= 1 unit
Step 2:
1 unit
= 42
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 42
= 126
2)
The ratio of the number of males to the number of females in an office was 4:5. After 15 females and 15 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer: 24
SOLUTION 1 :
Before
Males
:
Females
:
Difference
4x2
:
5x2
:
1x2
8
:
10
:
2
After
Males
:
Females
:
Difference
3
:
5
:
2
Step 1:
8 units - 3 units
= 5 units
Step 2:
5 units
= 15
1 unit
= 15 ÷ 5
= 3
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 3
= 24
3)
The ratio of the number of boys to the number of girls in a class was 3:4. After 66 girls and 66 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer: 176
SOLUTION 1 :
Before
Boys
:
Girls
:
Difference
3x2
:
4x2
:
1x2
6
:
8
:
2
After
Boys
:
Girls
:
Difference
3
:
5
:
2
Step 1:
6 units - 3 units
= 3 units
Step 2:
3 units
= 66
1 unit
= 66 ÷ 3
= 22
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 22
= 176
4)
The ratio of the number of males to the number of females in a stadium was 3:4. After 122 females and 122 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer: 183
SOLUTION 1 :
Before
Males
:
Females
:
Difference
3
:
4
:
1
After
Males
:
Females
:
Difference
1
:
2
:
1
Step 1:
3 units - 1 unit
= 2 units
Step 2:
2 units
= 122
1 unit
= 122 ÷ 2
= 61
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 61
= 183
5)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 29 childs and 29 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer: 203
SOLUTION 1 :
Before
Adults
:
Children
:
Difference
4
:
5
:
1
After
Adults
:
Children
:
Difference
3
:
4
:
1
Step 1:
4 units - 3 units
= 1 unit
1 unit
= 29
Step 2:
3 units + 4 units
= 7 units
Step 3:
7 units
= 7 x 29
= 203
6)
The ratio of the number of males to the number of females in a factory was 2:3. After 60 females and 60 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer: 180
SOLUTION 1 :
Before
Males
:
Females
:
Difference
2
:
3
:
1
After
Males
:
Females
:
Difference
1
:
2
:
1
Step 1:
2 units - 1 unit
= 1 unit
Step 2:
1 unit
= 60
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 60
= 180
7)
The ratio of the number of males to the number of females in an office was 4:5. After 20 females and 20 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer: 32
SOLUTION 1 :
Before
Males
:
Females
:
Difference
4x2
:
5x2
:
1x2
8
:
10
:
2
After
Males
:
Females
:
Difference
3
:
5
:
2
Step 1:
8 units - 3 units
= 5 units
Step 2:
5 units
= 20
1 unit
= 20 ÷ 5
= 4
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 4
= 32
8)
The ratio of the number of boys to the number of girls in a class was 3:4. After 72 girls and 72 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer: 192
SOLUTION 1 :
Before
Boys
:
Girls
:
Difference
3x2
:
4x2
:
1x2
6
:
8
:
2
After
Boys
:
Girls
:
Difference
3
:
5
:
2
Step 1:
6 units - 3 units
= 3 units
Step 2:
3 units
= 72
1 unit
= 72 ÷ 3
= 24
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 24
= 192
9)
The ratio of the number of males to the number of females in a stadium was 3:4. After 144 females and 144 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer: 216
SOLUTION 1 :
Before
Males
:
Females
:
Difference
3
:
4
:
1
After
Males
:
Females
:
Difference
1
:
2
:
1
Step 1:
3 units - 1 unit
= 2 units
Step 2:
2 units
= 144
1 unit
= 144 ÷ 2
= 72
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 72
= 216
10)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 30 childs and 30 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now