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 an office was 4:5. After 10 females and 10 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer:_______________
2)
The ratio of the number of males to the number of females in a factory was 2:3. After 35 females and 35 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer:_______________
3)
The ratio of the number of males to the number of females in a stadium was 3:4. After 62 females and 62 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer:_______________
4)
The ratio of the number of boys to the number of girls in a class was 3:4. After 30 girls and 30 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer:_______________
5)
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:_______________
6)
The ratio of the number of males to the number of females in an office was 4:5. After 25 females and 25 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer:_______________
7)
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:_______________
8)
The ratio of the number of males to the number of females in a stadium was 3:4. After 126 females and 126 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer:_______________
9)
The ratio of the number of boys to the number of girls in a class was 3:4. After 45 girls and 45 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer:_______________
10)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 21 childs and 21 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 an office was 4:5. After 10 females and 10 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer: 16
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
= 10
1 unit
= 10 ÷ 5
= 2
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 2
= 16
2)
The ratio of the number of males to the number of females in a factory was 2:3. After 35 females and 35 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer: 105
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
= 35
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 35
= 105
3)
The ratio of the number of males to the number of females in a stadium was 3:4. After 62 females and 62 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer: 93
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
= 62
1 unit
= 62 ÷ 2
= 31
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 31
= 93
4)
The ratio of the number of boys to the number of girls in a class was 3:4. After 30 girls and 30 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer: 80
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
= 30
1 unit
= 30 ÷ 3
= 10
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 10
= 80
5)
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: 210
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
= 30
Step 2:
3 units + 4 units
= 7 units
Step 3:
7 units
= 7 x 30
= 210
6)
The ratio of the number of males to the number of females in an office was 4:5. After 25 females and 25 males left the office, the new ratio became 3:5 respectively. How many workers are there in the office now
Answer: 40
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
= 25
1 unit
= 25 ÷ 5
= 5
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 5
= 40
7)
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
8)
The ratio of the number of males to the number of females in a stadium was 3:4. After 126 females and 126 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer: 189
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
= 126
1 unit
= 126 ÷ 2
= 63
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 63
= 189
9)
The ratio of the number of boys to the number of girls in a class was 3:4. After 45 girls and 45 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer: 120
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
= 45
1 unit
= 45 ÷ 3
= 15
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 15
= 120
10)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 21 childs and 21 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now