Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 Solutions: Introduction to Linear Polynomials

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 Solutions cover linear patterns from Introduction to Linear Polynomials. This exercise helps students form linear expressions from savings, rallies, rectangle area, box volume and pages-left situations.

Chapter 2 introduces linear polynomial Class 9 ideas through patterns where a quantity increases or decreases by a fixed amount. In Ganita Manjari Class 9 Chapter 2 Exercise 2.3, students learn how to represent real-life situations using a linear pattern Class 9 expression. These Class 9 Maths Chapter 2 Exercise 2.3 Solutions explain each question step by step so students can understand how algebraic expressions are formed from word problems.

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 Solutions: Introduction to Linear Polynomials

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 Solutions

Ex 2.3 Class 9 Ganita Manjari Solutions – Ganita Manjari Class 9 Exercise 2.3 Solutions

Question 1.
A student has ₹ 500 in her savings bank account. She gets ₹ 150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.

Solution:

The student initially has ₹500 in her savings account.
She gets ₹150 every month as pocket money.
At the end of the 1st month:
₹500 + ₹150 = ₹650
At the end of the 2nd month:
₹500 + 2 × ₹150 = ₹800
At the end of the 3rd month:
₹500 + 3 × ₹150 = ₹950
Similarly, at the end of the nth month:
Amount = 500 + 150n
Therefore, the required linear expression is:
150n + 500
Answer: The amount in the nth month is ₹(150n + 500).

Question 2.
A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1,2,3,… hours? Find a linear expression to represent the number of members at the end of the nth hour.

Solution:

The rally starts with 120 members.
Each hour, 9 members leave the group.
After 1 hour:
120 - 9 = 111 members
After 2 hours:
120 - 2 × 9 = 102 members
After 3 hours:
120 - 3 × 9 = 93 members
Therefore, after n hours:
Number of members = 120 - 9n
Answer: The linear expression is 120 - 9n.

Question 3.
Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.

Solution:

Length of the rectangle = 13 cm
Area of a rectangle = Length × Breadth
(i) When breadth = 12 cm:
Area = 13 × 12
= 156 cm²
(ii) When breadth = 10 cm:
Area = 13 × 10
= 130 cm²
(iii) When breadth = 8 cm:
Area = 13 × 8
= 104 cm²
If the breadth is represented by b cm, then:
Area = 13b
Answer: The linear expression representing the area of the rectangle is 13b.

Question 4.
Suppose the length of a rectangular box is 7 cm and the breadth is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm. Find the linear pattern representing the volume of the rectangular box.

Solution:

Length of the rectangular box = 7 cm
Breadth of the rectangular box = 11 cm
Volume of a rectangular box = Length × Breadth × Height
(i) When height = 5 cm:
Volume = 7 × 11 × 5
= 385 cm³
(ii) When height = 9 cm:
Volume = 7 × 11 × 9
= 693 cm³
(iii) When height = 13 cm:
Volume = 7 × 11 × 13
= 1001 cm³
If the height is represented by h cm, then:
Volume = 7 × 11 × h
= 77h
Answer: The linear expression representing the volume of the rectangular box is 77h.

Question 5.
Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.

Solution:

Sarita has a book of 500 pages.
She reads 20 pages every day.
Pages read in 15 days:
20 × 15 = 300 pages
Pages left:
500 - 300 = 200 pages
If the number of days is represented by n, then:
Pages left = 500 - 20n
Answer: After 15 days, 200 pages will be left. The linear expression is 500 - 20n.

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