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Introduction to Linear Polynomials Mathematics Ganita Manjari class 9 in English Medium ncert book solutions Exercise Set 2.3
Introduction to Linear Polynomials Exercise Set 2.3 – Complete NCERT Book Solutions for Class 9 Mathematics Ganita Manjari (English Medium). Get all chapter explanations, extra questions, solved examples and additional practice questions for Introduction to Linear Polynomials Exercise Set 2.3 to help you master concepts and score higher.
Introduction to Linear Polynomials Mathematics Ganita Manjari class 9 in English Medium ncert book solutions Exercise Set 2.3
NCERT Solutions for Class 9 Mathematics Ganita Manjari play an important role in helping students understand the concepts of the chapter Introduction to Linear Polynomials clearly. This chapter includes the topic Exercise Set 2.3, which is essential from both academic and examination point of view. The solutions provided here are prepared strictly according to the latest NCERT syllabus and follow the guidelines of CBSE to ensure accuracy and relevance. Each question is explained in a simple and student-friendly manner so that learners can grasp the concepts without confusion. These NCERT Solutions are useful for regular study, homework help, and exam preparation. All textbook questions are solved step by step to improve problem-solving skills and conceptual clarity. Students of Class 9 studying Mathematics Ganita Manjari can use these solutions to revise important topics, understand difficult questions, and practise effectively before examinations. The chapter Introduction to Linear Polynomials is explained in a structured way, making it easier for students to connect the theory with the topic Exercise Set 2.3. By studying these updated NCERT Solutions for Class 9 Mathematics Ganita Manjari, students can build a strong foundation, boost their confidence, and score better marks in school and board exams.
Introduction to Linear Polynomials
Exercise Set 2.3
Solve the following:
Q1. 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:
A student has ₹500 in her bank account and gets ₹150 every month as pocket money.
Amount at the end of each month
After 1 month:
500 + 150 = 650
After 2 months:
500 + 2(150) = 800
After 3 months:
500 + 3(150) = 950
Pattern:
650, 800, 950,…
Linear Expression
If n is the number of months, then:
A = 500 + 150n
So, the amount in the nth month is:
A = 500 + 150n
Q2. 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:
Initial members = 120
Every hour, 9 members leave.
Members remaining
After 1 hour:
120 − 9 = 111
After 2 hours:
120 − 18 = 102
After 3 hours:
120 − 27 = 93
Pattern:
111, 102, 93,…
Linear Expression
If n is the number of hours:
M = 120 − 9n
So, the number of members after nnn hours is:
M = 120 − 9n
Q3. 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 = 13 cm
(i) b = 12 cm
When Breadth = 12 cm
Area = Length x breadth
Area = 13 cm x 12 cm
= 156 cm2
(ii) b = 10 cm
When Breadth = 10 cm
Area = Length x breadth
Area = 13 cm x 10 cm
= 130 cm2
(ii) b = 8 cm
When Breadth = 8 cm
Area = Length x breadth
Area = 13 cm x 8 cm
= 104 cm2
Linear Pattern
If breadth =b
A=13b
So, the linear expression for area is:
A=13b
Q4. Suppose the length of a rectangular box is 7 cm and 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 = 7 cm
Breadth = 11 cm
Volume of rectangular box = Length × Breadth × Height
(i) h = 5 cm
When Height = 5 cm
Volume = Length × Breadth × Height
Volume = 7 cm × 11 cm × 5 cm
= 385 cm³
(ii) h = 9 cm
When Height = 9 cm
Volume = Length × Breadth × Height
Volume = 7 cm × 11 cm × 9 cm
= 693 cm³
(iii) h = 13 cm
When Height = 13 cm
Volume = Length × Breadth × Height
Volume = 7 cm × 11 cm × 13 cm
= 1001 cm³
Linear Pattern:
Volume = Length × Breadth × Height
V = 7 × 11 × h
V = 77h
Q5. 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:
Total pages in the book = 500
Pages read every day = 20
Number of days = 15
Pages read in 15 days
= 20 × 15
= 300
Pages left after 15 days
= 500 − 300
= 200
So, 200 pages will be left after 15 days.
Linear Pattern:
Let the number of days be d.
Pages left = Total pages − Pages read
P = 500 − 20d
See other sub-topics of this chapter:
1. Exercise Set 2.1 2. Exercise Set 2.2 3. Exercise Set 2.3 4. Exercise Set 2.4 5. Exercise Set 2.5 6. Exercise Set 2.6 7. Exercise Set 2.7