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

 Page 1


 
 
 
 
 
 
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