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 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:_______________
2)
The ratio of the number of males to the number of females in a factory was 2:3. After 10 females and 10 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 132 females and 132 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 adults to the number of childs in an amusement park was 4:5. After 12 childs and 12 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer:_______________
5)
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:_______________
6)
The ratio of the number of boys to the number of girls in a class was 3:4. After 81 girls and 81 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer:_______________
7)
The ratio of the number of males to the number of females in a factory was 2:3. After 31 females and 31 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 92 females and 92 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 adults to the number of childs in an amusement park was 4:5. After 24 childs and 24 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer:_______________
10)
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:_______________
1)
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
2)
The ratio of the number of males to the number of females in a factory was 2:3. After 10 females and 10 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer: 30
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
= 10
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 10
= 30
3)
The ratio of the number of males to the number of females in a stadium was 3:4. After 132 females and 132 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer: 198
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
= 132
1 unit
= 132 ÷ 2
= 66
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 66
= 198
4)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 12 childs and 12 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer: 84
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
= 12
Step 2:
3 units + 4 units
= 7 units
Step 3:
7 units
= 7 x 12
= 84
5)
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
6)
The ratio of the number of boys to the number of girls in a class was 3:4. After 81 girls and 81 boys left the class, the new ratio became 3:5 respectively. How many pupils are there in the class now
Answer: 216
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
= 81
1 unit
= 81 ÷ 3
= 27
Step 3:
3 units + 5 units
= 8 units
Step 4:
8 units
= 8 x 27
= 216
7)
The ratio of the number of males to the number of females in a factory was 2:3. After 31 females and 31 males left the factory, the new ratio became 1:2 respectively. How many workers are there in the factory now
Answer: 93
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
= 31
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 31
= 93
8)
The ratio of the number of males to the number of females in a stadium was 3:4. After 92 females and 92 males left the stadium, the new ratio became 1:2 respectively. How many spectators are there in the stadium now
Answer: 138
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
= 92
1 unit
= 92 ÷ 2
= 46
Step 3:
1 unit + 2 units
= 3 units
Step 4:
3 units
= 3 x 46
= 138
9)
The ratio of the number of adults to the number of childs in an amusement park was 4:5. After 24 childs and 24 adults left the amusement park, the new ratio became 3:4 respectively. How many visitors are there in the amusement park now
Answer: 168
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
= 24
Step 2:
3 units + 4 units
= 7 units
Step 3:
7 units
= 7 x 24
= 168
10)
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