Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 Solutions: Introduction to Linear Polynomials

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 Solutions cover evaluation of linear and quadratic polynomials, along with word problems based on linear equations. This exercise from Introduction to Linear Polynomials helps students substitute values in algebraic expressions and form equations from real-life situations.

Chapter 2 introduces students to linear polynomial Class 9 concepts through examples such as match fees, ages, coins, fencing and rectangle dimensions. In Ganita Manjari Class 9 Chapter 2 Exercise 2.2, students solve questions on the value of polynomial Class 9, linear equations and basic algebraic modelling. These Class 9 Maths Chapter 2 Exercise 2.2 Solutions explain each answer step by step in a clear, exam-ready format.

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 Solutions: Introduction to Linear Polynomials

Ex 2.2 Class 9 Ganita Manjari Chapter 2 Solutions

Question 1:
Find the value of the linear polynomial 5x – 3 if:
(i) x = 0

Solution:

Given the polynomial:

 

5x−35x - 3

 

For

x=0x = 0

:

 

5(0)−3=0−3=−35(0) - 3 = 0 - 3 = -3

 

Answer:

(ii) x = -1

Solution:

5x - 3 = 5(-1) - 3
= -5 - 3
= -8
Answer: -8

(iii) x = 2

Solution:

5x - 3 = 5(2) - 3
= 10 - 3
= 7
Answer: 7

Question 2.
Find the value of the quadratic polynomial 7s2 – 4s + 6 if:
(i) s = 0

Solution:

7(0)² - 4(0) + 6
= 0 - 0 + 6
= 6

(ii) s = -3

Solution:

7(-3)² - 4(-3) + 6
= 7(9) + 12 + 6
= 63 + 12 + 6
= 81

(iii) s = 4

Solution:

7(4)² - 4(4) + 6
= 7(16) - 16 + 6
= 112 - 16 + 6
= 102

Question 3.
The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Solution:

Let Salil’s present age be x years.
Then, his mother’s present age = 3x years.
After 5 years:
Salil’s age = x + 5
Mother’s age = 3x + 5
According to the question:
(x + 5) + (3x + 5) = 70
4x + 10 = 70
4x = 60
x = 15
Therefore:
Salil’s present age = 15 years
Mother’s present age = 3 × 15 = 45 years
Answer: Salil is 15 years old and his mother is 45 years old.

Question 4.
The difference between two positive integers is 63. The ratio of the two integers is 2 : 5. Find the two integers.

Solution:

Let the two integers be 2x and 5x.
According to the question:
5x - 2x = 63
3x = 63
x = 21
Therefore:
First integer = 2 × 21 = 42
Second integer = 5 × 21 = 105
Answer: The two integers are 42 and 105.

Question 5.
Ruby has 3 times as many two-rupee coins as she has five- rupee coins. If she has a total of 88, how many coins does she have of each type?

Solution:

Let the number of five-rupee coins be x.
Then, the number of two-rupee coins = 3x.
Value of five-rupee coins = 5x
Value of two-rupee coins = 2 × 3x = 6x
According to the question:
5x + 6x = 88
11x = 88
x = 8
Therefore,
Number of five-rupee coins = 8
Number of two-rupee coins = 3 × 8 = 24
Answer: Ruby has 8 five-rupee coins and 24 two-rupee coins.

Question 6.
A farmer cuts a 300-foot fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

Solution:

Let the length of the shorter piece be x feet.
Then, the length of the longer piece = 4x feet.
According to the question:
x + 4x = 300
5x = 300
x = 60
Therefore,
Shorter piece = 60 feet
Longer piece = 4 × 60 = 240 feet
Answer: The two pieces are 60 feet and 240 feet long.

Question 7.
If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

Solution:

Let the width of the rectangle be x cm.
Then, the length = 2x + 3 cm.
Perimeter of a rectangle = 2 × (Length + Width)
According to the question:
2[(2x + 3) + x] = 24
2(3x + 3) = 24
6x + 6 = 24
6x = 18
x = 3
Therefore,
Width = 3 cm
Length = 2(3) + 3
= 6 + 3
= 9 cm
Answer: The dimensions of the rectangle are 9 cm × 3 cm.

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