Well-designed AP 6th Class Maths Guide Chapter 12 Ratio and Proportion InText Questions offers step-by-step explanations to help students understand problem-solving strategies.
AP 7th Class Maths 12th Chapter Mensuration InText Questions
Try these (Page No: 152)
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?
Solution:
Number of boys in the class = 20
Number of girls in the class = 40
∴ Ratio of number of boys to the number of girls = \(\frac { 20 }{ 40 }\) = \(\frac { 1 }{ 2 }\)
Ratio = 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?
Solution:
Distance covered by Ravi = 6 km in an hour
Distance covered by Roshan = 4 km in an hour
Ratio of the distance covered by Ravi to the distance covered by Roshan
Try these (Page No: 154)
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.
Solution:
Time taken by Saurabh = 15 minutes
Time taken by Sachin = 1 hour = 60 minutes
(converting the time into same units)
∴ Ratio of the time taken by Saurabh to the time taken by Sachin
Ratio = 1 : 4
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.
Solution:
Cost of a toffee = 50 paise
Cost of a chocolate = ₹ 10
= 10 × 100 = 1000 paise
∴ The ratio of the cost of a toffee to the cost of chocolate
Ratio = 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 ?
Solution:
Number of holidays in one year = 73
Number of days in one year = 365
∴ Ratio of the number of holidays to days in one year =
Ratio = 1 : 5.
Try these (Page No: 158)
Question 1.
Find the ratio of number of notebooks to the number of books in your bag.
Solution:
Student’s Activity.
Question 2.
Find the ratio of number of desks and chairs in your classroom.
Solution:
Student’s Activity.
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.
Solution:
Student’s Activity.
Question 4.
Find the ratio of number of doors and the number of windows in your classroom.
Solution:
Student’s Activity.
Question 5.
Draw any rectangle and find the ratio of its length to its breadth.
Solution:
Student’s Activity.
Try these (Page No: 170)
Question 1.
Check whether the given ratios are equal, i.e. they are in proportion. If yes, then write them in the proper form.
1. 1 : 5 and 3 : 15
Solution:
1 : 5 and 3 : 15
3 : 15 = \(\frac { 3 }{ 15 }\) = \(\frac{3 /div 3}{15 /div 3}\) = \(\frac { 1 }{ 5 }\) = 1 : 5
So, 1 : 5 and 3 : 15 are equal ratios.
∴ Thus 1 : 5 : : 3 : 15
Question 2.
2 : 9 and 18 : 81
Solution:
2 : 9 and 18 : 81
18 : 81 = \(\frac { 18 }{ 81 }\) = \(\frac{18 /div 9}{81 /div 9}\) = \(\frac { 2 }{ 9 }\) = 2 : 9
So, 2 : 9 and 18 : 81 are equal ratios.
∴ Thus 2 : 9 :: 18 : 81
Question 3.
15 : 45 and 5 : 25
Solution:
15 : 45 and 5 : 25
15 : 45 = \(\frac { 15 }{ 45 }\) = \(\frac{15 /div 15}{45 /div 15}\) = \(\frac { 1 }{ 3 }\) = 1 : 3
5 : 25 = \(\frac { 5 }{ 25 }\) = \(\frac{5 /div 5}{25 /div 5}\) = \(\frac { 1 }{ 5 }\) = 1 : 5
Since 15 : 45 and 5 : 25 are not equal ratios.
15 : 45 and 5 : 25 are not in proportion.
Question 4.
4 : 12 and 9 : 27
Solution:
4 : 12 and 9 : 27
4 : 12 = \(\frac { 4 }{ 12 }\) = \(\frac{4 /div 4}{12 /div 4}\) = \(\frac { 1 }{ 3 }\) = 1 : 3
9 : 27 = \(\frac { 9 }{ 27 }\) = \(\frac{9 /div 9}{27 /div 9}\) = \(\frac { 1 }{ 3 }\) = 1 : 3
So, 4 : 12 and 9 : 27 are equal ratio
Thus 4 : 12 :: 9 : 27.
Question 5.
₹ 10 to ₹ 15 and 4 to 6
Solution:
₹ 10 to ₹ 15 and 4 to 6
Ratio of ₹ 10 to ₹ 15
= \(\frac{₹ 10}{₹ 15}\) = \(\frac{10}{15}\) = \(\frac{10 \div 5}{15 /div 5}\) = \(\frac { 2 }{ 3}\) = 2 : 3
Ratio of 4 to 6 = \(\frac{4}{6}\) = \(\frac{4 \div 2}{6 /div 2}\) = \(\frac { 2 }{ 3}\) = 2 : 3
So, ₹ 10 to ₹ 15 and 4 to 6 ratios are equal ratios.
₹ 10 : ₹ 15 :: 4 : 6
Try these (Page No: 176)
Question 1.
Prepare five similar problems and ask your friends to solve them,
Solution:
Student’s Activity.
Question 2.
Read the table and fill in the boxes.
Solution:
Distance travelled by Karan in 2 hours = 8 km
Distance travelled by Karan in 1 hour = \(\frac { 8 km }{ 2 }\) = 4 km
∴ Distance travelled by Karan in 4 hours = 4 km × 4 = 16 km
∴ _____ = 16 km
Distance travelled by Kriti in 2 hours = 6 km
Distance travelled by Kriti in 1 hour = \(\frac { 6 km }{ 2 }\) = 3 km
∴ _____ = 3 km
Distance travelled by Kriti in 1 hour = 3 km
∴ Distance travelled by Kriti in 4 hours = 3 km × 4 = 12 km
∴ _____ = 12 km