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.
Key Takeaways
Linear Pattern: A pattern is linear when the change is constant.
Fixed Increase: Savings and area examples show regular increase.
Fixed Decrease: Rally members and pages-left examples show regular decrease.
nth Term: A general expression gives the value for any stage, month or day.
Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 Solutions Structure 2026
| Exercise No. | Topic | Question Count |
| Exercise 2.3 | Monthly savings pattern | 1 |
| Exercise 2.3 | Rally members decreasing pattern | 1 |
| Exercise 2.3 | Rectangle area pattern | 1 |
| Exercise 2.3 | Rectangular box volume pattern | 1 |
| Exercise 2.3 | Pages-left linear pattern | 1 |
Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 Solutions
Exercise Set 2.3 is based on exploring linear patterns. A linear pattern is a sequence where the difference between consecutive terms is constant. In this exercise, students form expressions for money saved, members remaining in a rally, area of a rectangle, volume of a rectangular box and pages left in a book.
These Class 9 Maths linear patterns exercise answers help students connect algebraic expressions Class 9 with daily-life situations. The main idea is to identify the fixed starting value and the constant increase or decrease.
Exercise 2.3 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:
Initial amount in the bank account = ₹500
Pocket money received every month = ₹150
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
At the end of the 4th month:
500 + 4 × 150 = 1100
So, from the second month onwards, the amounts are:
| Month | Amount |
| 2 | ₹800 |
| 3 | ₹950 |
| 4 | ₹1100 |
| 5 | ₹1250 |
| 6 | ₹1400 |
For the nth month:
Amount = 500 + 150n
Answer: The linear expression is 500 + 150n. The amount from the second month onwards is ₹800, ₹950, ₹1100, ₹1250, ₹1400, ...
Exercise 2.3 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:
Initial number of rally members = 120
Number of members dropping out every hour = 9
After 1 hour:
120 − 9 = 111
After 2 hours:
120 − 2 × 9 = 102
After 3 hours:
120 − 3 × 9 = 93
After 4 hours:
120 − 4 × 9 = 84
So, the number of members remaining after 1, 2, 3, … hours is:
| Hours | Members Remaining |
| 1 | 111 |
| 2 | 102 |
| 3 | 93 |
| 4 | 84 |
| 5 | 75 |
For the nth hour:
Members remaining = 120 − 9n
Answer: The linear expression is 120 − 9n. The members remaining are 111, 102, 93, 84, 75, ...
Exercise 2.3 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 rectangle = 13 cm
Area of rectangle:
Area = length × breadth
(i) Breadth = 12 cm
Area = 13 × 12
Area = 156 cm²
(ii) Breadth = 10 cm
Area = 13 × 10
Area = 130 cm²
(iii) Breadth = 8 cm
Area = 13 × 8
Area = 104 cm²
If breadth is represented by b, then the area is:
A = 13b
Answer: The areas are 156 cm², 130 cm² and 104 cm². The linear pattern is A = 13b, where b is the breadth.
Exercise 2.3 Question 4
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 of rectangular box = 7 cm
Breadth of rectangular box = 11 cm
Volume of rectangular box:
Volume = length × breadth × height
So,
Volume = 7 × 11 × height
Volume = 77 × height
(i) Height = 5 cm
Volume = 77 × 5
Volume = 385 cm³
(ii) Height = 9 cm
Volume = 77 × 9
Volume = 693 cm³
(iii) Height = 13 cm
Volume = 77 × 13
Volume = 1001 cm³
If height is represented by h, then the volume is:
V = 77h
Answer: The volumes are 385 cm³, 693 cm³ and 1001 cm³. The linear pattern is V = 77h, where h is the height.
Exercise 2.3 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:
Total number of pages = 500
Pages read every day = 20
Pages read in 15 days:
20 × 15 = 300
Pages left after 15 days:
500 − 300 = 200
If the number of days is n, then pages left are:
Pages left = 500 − 20n
So, the linear pattern is:
P = 500 − 20n
where P is the number of pages left after n days.
Answer: After 15 days, 200 pages will be left. The linear pattern is P = 500 − 20n.
Final Answers for Exercise 2.3
| Question | Final Answer |
| 1 | Linear expression: 500 + 150n |
| 1 | Amount from 2nd month onwards: ₹800, ₹950, ₹1100, ₹1250, ₹1400, ... |
| 2 | Linear expression: 120 − 9n |
| 2 | Members remaining: 111, 102, 93, 84, 75, ... |
| 3(i) | 156 cm² |
| 3(ii) | 130 cm² |
| 3(iii) | 104 cm² |
| 3 | Linear pattern: A = 13b |
| 4(i) | 385 cm³ |
| 4(ii) | 693 cm³ |
| 4(iii) | 1001 cm³ |
| 4 | Linear pattern: V = 77h |
| 5 | Pages left after 15 days = 200 |
| 5 | Linear pattern: P = 500 − 20n |
Concept Used in Introduction to Linear Polynomials Exercise 2.3
Introduction to Linear Polynomials Exercise 2.3 is based on linear patterns. A linear pattern is formed when a quantity increases or decreases by the same amount each time.
Important points:
- If a quantity increases by a fixed amount, the pattern is linear.
- If a quantity decreases by a fixed amount, the pattern is also linear.
- A linear pattern can be written using a linear expression Class 9 form.
- Expressions such as 500 + 150n, 120 − 9n, A = 13b, V = 77h and P = 500 − 20n are examples of linear expressions.
- These expressions are connected to linear polynomial Class 9 because the variable has power 1.
These ideas are important for Class 9 Ganita Manjari linear polynomials solutions because later sections use linear growth, linear decay and linear relationships.
About Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3
Ganita Manjari Class 9 Chapter 2 Exercise 2.3 appears in the section “Exploring Linear Patterns”. It comes after students learn how a growing tile pattern can be represented by the expression 2n − 1.
These Class 9 Maths Chapter 2 Exercise 2.3 Solutions prepare students for:
- linear patterns,
- linear growth,
- linear decay,
- linear expressions,
- real-life algebraic modelling,
- linear relationships,
- and equations of the form y = ax + b.
NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2
| Section | NCERT Solutions |
| Class 9 Maths Ganita Manjari 2026 | NCERT Class 9 Maths Ganita Manjari 2026 |
| Chapter 2 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 |
| Exercise 2.1 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.1 |
| Exercise 2.2 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 |
| Exercise 2.3 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.3 |
| Exercise 2.4 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.4 |
| Exercise 2.5 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.5 |
| Exercise 2.6 | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.6 |
| End of Chapter Exercises | NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 End of Chapter Exercises |
FAQs (Frequently Asked Questions)
To write a linear pattern, first identify the starting value and then find how much the value increases or decreases each time. For example, if a student starts with ₹500 and gets ₹150 every month, the amount after n months is 500 + 150n.
In Exercise 2.3, n usually represents the number of months, hours or days. For example, in 120 − 9n, n represents the number of hours after the rally starts.
Check whether the quantity is being added or subtracted each time. In 500 + 150n, the amount increases, so it is an increasing pattern. In 120 − 9n, the number of members decreases, so it is a decreasing pattern.
The rally starts with 120 members, and 9 members drop out every hour. So, after n hours, the number of members remaining is 120 − 9n.
The length of the rectangle is fixed at 13 cm, and only the breadth changes. Since Area = 13 × breadth, the area changes at a constant rate. That is why A = 13b is a linear pattern.