Objective Type Questions: Ratio, Proportion and Unitary Method

# Objective Type Questions: Ratio, Proportion and Unitary Method | Mathematics (Maths) Class 6 PDF Download

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Objective Type Questions                                                    page: 9.19
Mark the correct alternative in each of the following:

1. A ratio equivalent of 2 : 3 is
(a) 4 : 3
(b) 2 : 6
(c) 6 : 9
(d) 10 : 9
Solution:

The option (c) is correct answer.
We know that 6: 9 when divided by 3 we get 2: 3.

2. The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Solution:

The option (c) is correct answer.
We know that the sum of all the angles = 180°
So the largest angle = 3/ (1 + 2 + 3) × 180
We get
Largest angle = 3/6 × 180 = 90°

3. The sides of a triangle are in the ratio 2 : 3 : 5. If its perimeter is 100 cm, the length of its smallest side is
(a) 2 cm
(b) 20 cm
(c) 3 cm
(d) 5 cm
Solution:

The option (b) is correct answer.
We know that the length of smallest side = 100 × 2/ (2 + 3 + 5) = 200/10 = 20 cm

4. Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is
(a) 63
(b) 42
(c) 49
(d) 72
Solution:

The option (a) is correct answer.
Consider x as the largest number
So we get
7x + 9x = 112
16x = 112
x = 112/16 = 7
Page 2

Objective Type Questions                                                    page: 9.19
Mark the correct alternative in each of the following:

1. A ratio equivalent of 2 : 3 is
(a) 4 : 3
(b) 2 : 6
(c) 6 : 9
(d) 10 : 9
Solution:

The option (c) is correct answer.
We know that 6: 9 when divided by 3 we get 2: 3.

2. The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Solution:

The option (c) is correct answer.
We know that the sum of all the angles = 180°
So the largest angle = 3/ (1 + 2 + 3) × 180
We get
Largest angle = 3/6 × 180 = 90°

3. The sides of a triangle are in the ratio 2 : 3 : 5. If its perimeter is 100 cm, the length of its smallest side is
(a) 2 cm
(b) 20 cm
(c) 3 cm
(d) 5 cm
Solution:

The option (b) is correct answer.
We know that the length of smallest side = 100 × 2/ (2 + 3 + 5) = 200/10 = 20 cm

4. Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is
(a) 63
(b) 42
(c) 49
(d) 72
Solution:

The option (a) is correct answer.
Consider x as the largest number
So we get
7x + 9x = 112
16x = 112
x = 112/16 = 7

Here
7x = 7 × 7 = 49
9x = 9 × 7 = 63
Hence, the largest number is 63.

5. Two ratio 384 : 480 in its simplest form is
(a) 3 : 5
(b) 5 : 4
(c) 4 : 5
(d) 2 : 5
Solution:

The option (c) is correct answer.
384: 480 can be written as
384/480 = 4/5 when divided by 96

6. If A, B, C, divide Rs 1200 in the ratio 2 : 3 : 5, then B's share is
(a) Rs 240
(b) Rs 600
(c) Rs 380
(d) Rs 360
Solution:

The option (d) is correct answer.
So B’s share = 1200 × 3/ (2 + 3 + 5)
On further calculation
B’s share = 1200 × 3/10 = Rs 360

7. If a bus travels 126 km in 3 hours and a train travels 315 km in 5 hours, then the ratio of their speeds is
(a) 2 : 5
(b) 2 : 3
(c) 5 : 2
(d) 25 : 6
Solution:

The option (b) is correct answer.
We know that speed = distance/time
So the speed of bus = 126/3 = 42 km/h
Speed of train = 315/5 = 63 km/h
So the ratio of their speeds = 42: 63 = 2: 3

8. The ratio of male and female employees in a multinational company is 5 : 3. If there are 115 male
employees in the company, then the number of female employees is
(a) 96
(b) 52
(c) 69
(d) 66
Solution:

The option (c) is correct answer.
Page 3

Objective Type Questions                                                    page: 9.19
Mark the correct alternative in each of the following:

1. A ratio equivalent of 2 : 3 is
(a) 4 : 3
(b) 2 : 6
(c) 6 : 9
(d) 10 : 9
Solution:

The option (c) is correct answer.
We know that 6: 9 when divided by 3 we get 2: 3.

2. The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Solution:

The option (c) is correct answer.
We know that the sum of all the angles = 180°
So the largest angle = 3/ (1 + 2 + 3) × 180
We get
Largest angle = 3/6 × 180 = 90°

3. The sides of a triangle are in the ratio 2 : 3 : 5. If its perimeter is 100 cm, the length of its smallest side is
(a) 2 cm
(b) 20 cm
(c) 3 cm
(d) 5 cm
Solution:

The option (b) is correct answer.
We know that the length of smallest side = 100 × 2/ (2 + 3 + 5) = 200/10 = 20 cm

4. Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is
(a) 63
(b) 42
(c) 49
(d) 72
Solution:

The option (a) is correct answer.
Consider x as the largest number
So we get
7x + 9x = 112
16x = 112
x = 112/16 = 7

Here
7x = 7 × 7 = 49
9x = 9 × 7 = 63
Hence, the largest number is 63.

5. Two ratio 384 : 480 in its simplest form is
(a) 3 : 5
(b) 5 : 4
(c) 4 : 5
(d) 2 : 5
Solution:

The option (c) is correct answer.
384: 480 can be written as
384/480 = 4/5 when divided by 96

6. If A, B, C, divide Rs 1200 in the ratio 2 : 3 : 5, then B's share is
(a) Rs 240
(b) Rs 600
(c) Rs 380
(d) Rs 360
Solution:

The option (d) is correct answer.
So B’s share = 1200 × 3/ (2 + 3 + 5)
On further calculation
B’s share = 1200 × 3/10 = Rs 360

7. If a bus travels 126 km in 3 hours and a train travels 315 km in 5 hours, then the ratio of their speeds is
(a) 2 : 5
(b) 2 : 3
(c) 5 : 2
(d) 25 : 6
Solution:

The option (b) is correct answer.
We know that speed = distance/time
So the speed of bus = 126/3 = 42 km/h
Speed of train = 315/5 = 63 km/h
So the ratio of their speeds = 42: 63 = 2: 3

8. The ratio of male and female employees in a multinational company is 5 : 3. If there are 115 male
employees in the company, then the number of female employees is
(a) 96
(b) 52
(c) 69
(d) 66
Solution:

The option (c) is correct answer.

Consider x as the number of female employees
So we get
5/3 = 115/x
By cross multiplication
5x = 115 × 3 = 345
By division
x = 345/5 = 69

9. Length and width of a field are in the ratio 5 : 3. If the width of the field is 42 m, then its length is
(a) 50 m
(b) 70 m
(c) 80 m
(d) 100 m
Solution:

The option (b) is correct answer.
It is given that length and width of a field = 5: 3
Consider x m as the length
Width of the filed = 42 m
So the length can be written as
5/3 = x/42
By cross multiplication
3x = 42 × 5 = 210
By division
x = 210/3 = 70

10. If 57 : x = 51 : 85, then the value of x is
(a) 95
(b) 76
(c) 114
(d) None of these
Solution:

The option (a) is correct answer.
It can be written as
57/x = 51/85
By cross multiplication
57 × 85/51 = x
So we get
x = 95

11. The ratio of boys and girls in a school is 12 : 5. If there are 840 girls in the school, then the number of
boys is
(a) 1190
(b) 2380
(c) 2856
(d) 2142
Solution:

The options are not correct.
Page 4

Objective Type Questions                                                    page: 9.19
Mark the correct alternative in each of the following:

1. A ratio equivalent of 2 : 3 is
(a) 4 : 3
(b) 2 : 6
(c) 6 : 9
(d) 10 : 9
Solution:

The option (c) is correct answer.
We know that 6: 9 when divided by 3 we get 2: 3.

2. The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Solution:

The option (c) is correct answer.
We know that the sum of all the angles = 180°
So the largest angle = 3/ (1 + 2 + 3) × 180
We get
Largest angle = 3/6 × 180 = 90°

3. The sides of a triangle are in the ratio 2 : 3 : 5. If its perimeter is 100 cm, the length of its smallest side is
(a) 2 cm
(b) 20 cm
(c) 3 cm
(d) 5 cm
Solution:

The option (b) is correct answer.
We know that the length of smallest side = 100 × 2/ (2 + 3 + 5) = 200/10 = 20 cm

4. Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is
(a) 63
(b) 42
(c) 49
(d) 72
Solution:

The option (a) is correct answer.
Consider x as the largest number
So we get
7x + 9x = 112
16x = 112
x = 112/16 = 7

Here
7x = 7 × 7 = 49
9x = 9 × 7 = 63
Hence, the largest number is 63.

5. Two ratio 384 : 480 in its simplest form is
(a) 3 : 5
(b) 5 : 4
(c) 4 : 5
(d) 2 : 5
Solution:

The option (c) is correct answer.
384: 480 can be written as
384/480 = 4/5 when divided by 96

6. If A, B, C, divide Rs 1200 in the ratio 2 : 3 : 5, then B's share is
(a) Rs 240
(b) Rs 600
(c) Rs 380
(d) Rs 360
Solution:

The option (d) is correct answer.
So B’s share = 1200 × 3/ (2 + 3 + 5)
On further calculation
B’s share = 1200 × 3/10 = Rs 360

7. If a bus travels 126 km in 3 hours and a train travels 315 km in 5 hours, then the ratio of their speeds is
(a) 2 : 5
(b) 2 : 3
(c) 5 : 2
(d) 25 : 6
Solution:

The option (b) is correct answer.
We know that speed = distance/time
So the speed of bus = 126/3 = 42 km/h
Speed of train = 315/5 = 63 km/h
So the ratio of their speeds = 42: 63 = 2: 3

8. The ratio of male and female employees in a multinational company is 5 : 3. If there are 115 male
employees in the company, then the number of female employees is
(a) 96
(b) 52
(c) 69
(d) 66
Solution:

The option (c) is correct answer.

Consider x as the number of female employees
So we get
5/3 = 115/x
By cross multiplication
5x = 115 × 3 = 345
By division
x = 345/5 = 69

9. Length and width of a field are in the ratio 5 : 3. If the width of the field is 42 m, then its length is
(a) 50 m
(b) 70 m
(c) 80 m
(d) 100 m
Solution:

The option (b) is correct answer.
It is given that length and width of a field = 5: 3
Consider x m as the length
Width of the filed = 42 m
So the length can be written as
5/3 = x/42
By cross multiplication
3x = 42 × 5 = 210
By division
x = 210/3 = 70

10. If 57 : x = 51 : 85, then the value of x is
(a) 95
(b) 76
(c) 114
(d) None of these
Solution:

The option (a) is correct answer.
It can be written as
57/x = 51/85
By cross multiplication
57 × 85/51 = x
So we get
x = 95

11. The ratio of boys and girls in a school is 12 : 5. If there are 840 girls in the school, then the number of
boys is
(a) 1190
(b) 2380
(c) 2856
(d) 2142
Solution:

The options are not correct.

Consider x as the number of boys
Ratio of boys and girls = 12: 5
It can be written as
12/5 = x/840
By cross multiplication
x = 12/5 × 840 = 2016

12. If 4, a, a, 36 are in proportion, then a =
(a) 24
(b) 12
(c) 3
(d) 24
Solution:

The option (b) is correct answer.
It is given that 4, a, a, 36 are in proportion
We can write it as 4 : a :: a : 36
So we get
4/a = a/36
By cross multiplication
4 × 36 = a × a
We get
a
2
= 144
So a = 12

13. If 5 : 4 : : 30 : x, then the value of x is
(a) 24
(b) 12
(c) 3/2
(d) 6
Solution:

The option (a) is correct answer.
It can be written as
5/4 = 30/x
By cross multiplication
x = 30 × 4/5 = 24

14. If a, b, c, d are in proportion, then
(a) ab = cd
(b) ac = bd
(c) ad = bc
(d) None of these
Solution:

The option (c) is correct answer.
It is given that a, b, c, d are in proportion
We can write it as a : b :: c : d
So we get
a/b = c/d
Page 5

Objective Type Questions                                                    page: 9.19
Mark the correct alternative in each of the following:

1. A ratio equivalent of 2 : 3 is
(a) 4 : 3
(b) 2 : 6
(c) 6 : 9
(d) 10 : 9
Solution:

The option (c) is correct answer.
We know that 6: 9 when divided by 3 we get 2: 3.

2. The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Solution:

The option (c) is correct answer.
We know that the sum of all the angles = 180°
So the largest angle = 3/ (1 + 2 + 3) × 180
We get
Largest angle = 3/6 × 180 = 90°

3. The sides of a triangle are in the ratio 2 : 3 : 5. If its perimeter is 100 cm, the length of its smallest side is
(a) 2 cm
(b) 20 cm
(c) 3 cm
(d) 5 cm
Solution:

The option (b) is correct answer.
We know that the length of smallest side = 100 × 2/ (2 + 3 + 5) = 200/10 = 20 cm

4. Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is
(a) 63
(b) 42
(c) 49
(d) 72
Solution:

The option (a) is correct answer.
Consider x as the largest number
So we get
7x + 9x = 112
16x = 112
x = 112/16 = 7

Here
7x = 7 × 7 = 49
9x = 9 × 7 = 63
Hence, the largest number is 63.

5. Two ratio 384 : 480 in its simplest form is
(a) 3 : 5
(b) 5 : 4
(c) 4 : 5
(d) 2 : 5
Solution:

The option (c) is correct answer.
384: 480 can be written as
384/480 = 4/5 when divided by 96

6. If A, B, C, divide Rs 1200 in the ratio 2 : 3 : 5, then B's share is
(a) Rs 240
(b) Rs 600
(c) Rs 380
(d) Rs 360
Solution:

The option (d) is correct answer.
So B’s share = 1200 × 3/ (2 + 3 + 5)
On further calculation
B’s share = 1200 × 3/10 = Rs 360

7. If a bus travels 126 km in 3 hours and a train travels 315 km in 5 hours, then the ratio of their speeds is
(a) 2 : 5
(b) 2 : 3
(c) 5 : 2
(d) 25 : 6
Solution:

The option (b) is correct answer.
We know that speed = distance/time
So the speed of bus = 126/3 = 42 km/h
Speed of train = 315/5 = 63 km/h
So the ratio of their speeds = 42: 63 = 2: 3

8. The ratio of male and female employees in a multinational company is 5 : 3. If there are 115 male
employees in the company, then the number of female employees is
(a) 96
(b) 52
(c) 69
(d) 66
Solution:

The option (c) is correct answer.

Consider x as the number of female employees
So we get
5/3 = 115/x
By cross multiplication
5x = 115 × 3 = 345
By division
x = 345/5 = 69

9. Length and width of a field are in the ratio 5 : 3. If the width of the field is 42 m, then its length is
(a) 50 m
(b) 70 m
(c) 80 m
(d) 100 m
Solution:

The option (b) is correct answer.
It is given that length and width of a field = 5: 3
Consider x m as the length
Width of the filed = 42 m
So the length can be written as
5/3 = x/42
By cross multiplication
3x = 42 × 5 = 210
By division
x = 210/3 = 70

10. If 57 : x = 51 : 85, then the value of x is
(a) 95
(b) 76
(c) 114
(d) None of these
Solution:

The option (a) is correct answer.
It can be written as
57/x = 51/85
By cross multiplication
57 × 85/51 = x
So we get
x = 95

11. The ratio of boys and girls in a school is 12 : 5. If there are 840 girls in the school, then the number of
boys is
(a) 1190
(b) 2380
(c) 2856
(d) 2142
Solution:

The options are not correct.

Consider x as the number of boys
Ratio of boys and girls = 12: 5
It can be written as
12/5 = x/840
By cross multiplication
x = 12/5 × 840 = 2016

12. If 4, a, a, 36 are in proportion, then a =
(a) 24
(b) 12
(c) 3
(d) 24
Solution:

The option (b) is correct answer.
It is given that 4, a, a, 36 are in proportion
We can write it as 4 : a :: a : 36
So we get
4/a = a/36
By cross multiplication
4 × 36 = a × a
We get
a
2
= 144
So a = 12

13. If 5 : 4 : : 30 : x, then the value of x is
(a) 24
(b) 12
(c) 3/2
(d) 6
Solution:

The option (a) is correct answer.
It can be written as
5/4 = 30/x
By cross multiplication
x = 30 × 4/5 = 24

14. If a, b, c, d are in proportion, then
(a) ab = cd
(b) ac = bd
(c) ad = bc
(d) None of these
Solution:

The option (c) is correct answer.
It is given that a, b, c, d are in proportion
We can write it as a : b :: c : d
So we get
a/b = c/d

By cross multiplication
ad = bc

15. If a, b, c, are in proportion, then
(a) a
2
= bc
(b) b
2
= ac
(c) c
2
= ab
(d) None of these
Solution:

The option (b) is correct answer.
It is given that a, b, c are in proportion
We can write it as
a : b :: b : c
So we get
a/b = b/c
By cross multiplication
b
2
= ac

16. If the cost of 5 bars of a soap is Rs. 30, then the cost of one dozen bars is
(a) Rs 60
(b) Rs 120
(c) Rs 72
(d) Rs 140
Solution:

The option (c) is correct answer.
Consider Rs x as the cost of one dozen bars
It can be written as
30/5 = x/12
So we get
x = 30/5 × 12 = Rs 72

17. 12 men can finish a piece of work in 25 days. The number of days in which the same piece of work can
be done by 20 men, is
(a) 10 days
(b) 12 days
(c) 15 days
(d) 14 days
Solution:

The option (c) is correct answer.
Consider x days required by 20 men to do the same work
20/12 = 25/x
So we get
x = 12 × 25/20 = 15 days

18. If the cost of 25 packets of 12 pencils each is Rs 750, then the cost of 30 packets of 8 pencils each is
(a) Rs 600
(b) Rs 720
```

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

## FAQs on Objective Type Questions: Ratio, Proportion and Unitary Method - Mathematics (Maths) Class 6

 1. What is a ratio and how is it calculated?
A ratio is a comparison of two quantities. It is calculated by dividing one quantity by another quantity. For example, if there are 4 red balls and 6 blue balls, the ratio of red balls to blue balls is 4:6 or simplified as 2:3.
 2. How is proportion related to ratio?
Proportion is a statement that two ratios are equal. It is used to compare two ratios and determine if they are equivalent. For example, if the ratio of red balls to blue balls is 2:3 and the ratio of green balls to yellow balls is 6:9, we can set up the proportion 2:3 = 6:9 and solve for the missing values.
 3. What is the unitary method and how is it used?
The unitary method is a technique used to solve problems involving ratios and proportions. It involves finding the value of one unit and then using that value to find the value of another unit. For example, if the cost of 5 pens is \$10, we can find the cost of 1 pen by dividing \$10 by 5, which gives us \$2. We can then use this value to find the cost of any number of pens.
 4. How do you solve problems involving direct proportion?
To solve problems involving direct proportion, you need to set up a proportion and solve for the missing value. For example, if the distance travelled is directly proportional to the time taken, and it takes 4 hours to travel 240 miles, we can set up the proportion 4:240 = x:6 (where x is the unknown distance). Cross-multiplying and solving for x gives us x = 36, so the distance travelled in 6 hours is 36 miles.
 5. How can I use the unitary method to convert between units of measurement?
To convert between units of measurement using the unitary method, you need to establish a ratio between the two units. For example, if 1 meter is equal to 100 centimeters, and you want to convert 5 meters to centimeters, you can set up the proportion 1:100 = 5:x (where x is the unknown value in centimeters). Cross-multiplying and solving for x gives us x = 500, so 5 meters is equal to 500 centimeters.

## Mathematics (Maths) Class 6

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