Introduction to Linear Polynomials Class 9 Mathematics Ganita Manjari [LATEST] Solutions Exercise Set 2.3 in English - CBSE Study
NCERT Solutions for Class 9 Mathematics Ganita Manjari are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important Introduction to Linear Polynomials with detailed explanations and step-by-step answers for better exam preparation. Each Exercise Set 2.3 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 9 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics Ganita Manjari.
Class 9 English Medium Mathematics Ganita Manjari All Chapters:
Introduction to Linear Polynomials
3. 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
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