These NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion InText Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion InText Questions
NCERT In-text Question Page No. 245
Question 1.
In a class, there are 20 boys and 40 girls. What is the ratio of the number of boys to the number of girls?
Answer:
Number of boys = 20
Number of girls = 40
Ratio of boys to girls = \(\frac{20}{40}=\frac{1}{2}=\frac{1}{2}\)
hence the required ratio is \(\frac{1}{2}\)
Question 2.
Ravi walks 6 km in an hour while Roshan walks 4 km in an hour. What is the ratio of the distance covered by Ravi to the distance covered by Roshan?
Answer:
Distance covered by Ravi in 1 hr = 6 km
Distance covered by Roshan in 1 hr = 4 km
∴ Ratio of distance covered Ravi in 1 hr to distance covered by Roshan in 1 hr = 6 km : 4
= \(\frac{6}{3}=\frac{4}{2}\)
Note:
(i) We donate ratio by the symbol
(ii) Ratio has no unit.
(iii) Two quantities can be compared only if they are in the same unit.
(iv) In a ratio the order of terms is very important. 2 : 3 and 3 : 2 are different ratios.
NCERT In-text Question Page No. 246
Question 1.
Saurabh takes 15 minutes to reach school from his house and Sachin takes one hour to reach school from his house. Find the ratio of the time taken by Saurabh to the time taken by Sachin.
Answer:
Time taken by Saurab = 15 minutes
Time taken by Sachin = 1 hour = 60 minutes
∴ Ratio of time taken by Saurabh to the time taken by Sachin
= \(\frac{\text { Time taken by Saurabh }}{\text { Time taken by Sachin }}\)
= \(\frac{15}{10}=\frac{15 \div 15}{60 \div 15}=\frac{1}{4}\) 1 : 4
[∵ HCF of 15 and 60 is 15]
Question 2.
Cost of a toffee is 50 paise and cost of a chocolate is ₹ 10. Find the ratio of the cost of a toffee to the cost of a chocolate.
Answer:
Cost of Toffee = 50 paise
Cost of chocolate = ₹ 10 rupees
[∵ ₹ 1 = 100 paise]
∴ 10 ₹ = 1000 paise
So, the cost of chocolate = 1000 paise
The ratio of the cost of toffee to the cost of chocolate = \(\frac{50}{1000}\) = 1 : 20
Question 3.
In a school, there were 73 holidays in one year. What is the ratio of the number of holidays to the number of days in one year?
Answer:
Number of holidays = 73 days
Number of days in one year = 365 days
[∵ HCF of 73 and 365 is 73]
NCERT In-text Question Page No. 248
Question 1.
Find the ratio of number of notebooks to the number of books in your bag.
Answer:
It is activity, please do it yourself.
Question 2.
Find the ratio of number of desks and chairs in your classroom.
Answer:
It is activity, please do it yourself.
Question 3.
Find the number of students above twelve years of age in your class. Then, find the ratio of number of students with age above twelve years and the remaining students.
Answer:
It is activity, please do it yourself.
Question 4.
Find the ratio of number of doors and the number of windows in your classroom.
Answer:
It is activity, please do it yourself.
Question 5.
Draw any rectangle and find the ratio of its length to its breadth.
Answer:
It is activity, please do it yourself.
NCERT In-text Question Page No. 254
Question 1.
Determine if the following are in proportion.
If yes, then write them in the proper form.
1. 1 : 5 and 3 : 15
2. 2 : 9 and 18 : 81
3. 15 : 45 and 5 : 25
4. 4 : 12 and 9 : 27
5. ₹ 10 to ₹15 and 4 to 6
Answer:
1. 1 : 5 and 3 : 15
We have, 3 : 15 = \(\frac{3}{15}=\frac{3 \div 3}{15 \div 3}=\frac{1}{5}\) = 1 : 5
[ ∵ HFC of 3 and 15 is 3]
i.e,. 1 : 5 and 3 : 15 are in proportion.
Thus, the proper form is 1 : 5 :: 3 : 15
2. 2 : 9 and 18 : 81
We have, 18 : 81= \(\frac{18}{81}=\frac{18 \div 9}{81 \div 9}=\frac{2}{9}\) = 2 : 9
[∵ HFC of 18 and 81 is 9]
i. e,. 2 : 9 and 18:81 are in proportion.
Thus, the proper form is 2 : 9 :: 18:81
3. 15 : 45 and 5 : 25
We have, 15 : 45 = \(\frac{15}{45}=\frac{15 \div 15}{45 \div 15}=\frac{1}{3}\) = 1 : 3
[ ∵ HFC of 15 and 45 is 15]
We have, 5 : 25 = \(\frac{5}{25}=\frac{5 \div 5}{25 \div 5}=\frac{1}{5}\) = 1 : 5
[∵HCF of 5 and 25 is 5]
∵ 1 : 3 ≠ 1 : 5 ∴ 15 : 45 ≠ 5 : 25
i. e,. 15 : 45 and 5 : 25 are not in proportion.
4. 4 : 12 and 9: 27
We have, 4 : 12 = \(\frac{4}{12}=\frac{4 \div 4}{12 \div 4}=\frac{1}{3}\) = 1 : 3
[∵ HFC of 4 and 12 is 4]
Again we have, 9 : 27 = \(\frac{9}{27}=\frac{9 \div 9}{27 \div 9}=\frac{1}{3}\) =1:3
[∵ HFC of 9 and 27 is 9]
4 : 12 = 9 : 27
or 4 : 12 and 9 : 27 are in proportion,
i.e., 4 : 12 : : 9 : 27 is the correct form.
5. ₹ 10 to ₹ 15 and 4 to 6
We have, ₹10 : ₹15 = \(=\frac{10}{15}=\frac{10 \div 5}{15 \div 5}=\frac{2}{3}\) = 2 : 3
[∵ HCF of 10 and 15 is 5]
Again we have, 4 : 6 = \(\frac{4}{6}=\frac{4 \div 2}{6 \div 2}=\frac{2}{3}\) = 1 : 3
[∵ HFC of 4 and 6 is 2]
Thus ₹ 10 : ₹ 15 = 4 : 6.
or ₹ 10, ₹ 15, 4 and 6 are in proportion.
so, the correct from is ₹ 10 : ₹ 15 : : 4 : 6
NCERT In-text Question Page No. 257
Question 1.
Prepare five similar problems (on unitary method) and ask your friends to solve them.
Answer:
It is a project work. Please do it yourself.
Question 2.
Read the table and fill in the boxes
Answer:
∵ Distance travelled by Kriti in 2 hours = 6 km
∴ Distance travelled by Kriti in 1 hour = \(\frac { 6 }{ 2 }\) = 3 km
∴ Distance travelled by Karan in 1 hour = 5 km
∴ Distance travelled by Karan in 4 hours = 4 x 4 km = 16 km
∴ Distance travelled by Kriti in 1 hour = 3 km
∴ Distance travelled by Kriti in 4 hour = 3 x 4 km = 12 km
Thus, the table is written as given below :
