---
title: "NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.3"
url: https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-3
dateModified: 2026-10-07T15:41:27+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.3

Chapter 2: Introduction to Linear Polynomials. Every question from Exercise 2.3, with full working and the final answer.

Free PDF (24 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-9/swavid-ncert-solutions-class-9-maths-chapter-2-introduction-to-linear-polynomials-1ce112dddf.pdf

## Exercise Set 2.3

### Question 1

*3 marks · Short answer*

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 $n^{\text{th}}$ month.

**Part (i)**

1. At the end of the 1st month, the amount is ₹$(500 + 150 \times 1) = \text{₹}650$.
2. At the end of the 2nd month, the amount is ₹$(500 + 150 \times 2) = \text{₹}800$.
3. At the end of the 3rd month, the amount is ₹$(500 + 150 \times 3) = \text{₹}950$.

Answer (i): ₹650, ₹800, and ₹950

**Part (ii)**

1. Initial amount = ₹500 and monthly addition = ₹150.
2. For $n$ months, the total addition is ₹$150n$.
3. Thus, the linear expression representing the amount in the $n^{\text{th}}$ month is ₹$(500 + 150n)$.

Answer (ii): ₹$(500 + 150n)$

**Answer:** The amount at the end of month $n$ is ₹$(500 + 150n)$.

> Common mistake: Including the initial amount multiplied by $n$ or missing the initial fixed amount.

### Question 2

*3 marks · Short answer*

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 $n^{\text{th}}$ hour.

**Part (i)**

1. After 1 hour, remaining members = $120 - 9 \times 1 = 111$.
2. After 2 hours, remaining members = $120 - 9 \times 2 = 102$.
3. After 3 hours, remaining members = $120 - 9 \times 3 = 93$.

Answer (i): 111, 102, and 93 members

**Part (ii)**

1. Initial members = 120 and members leaving every hour = 9.
2. After $n$ hours, total members leaving = $9n$.
3. Thus, the linear expression for the remaining members is $120 - 9n$.

Answer (ii): $120 - 9n$

**Answer:** The number of members remaining after $n$ hours is $120 - 9n$.

> Common mistake: Adding the rate of decrease instead of subtracting it.

### Question 3

*3 marks · Short answer*

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.

**Part (i)**

1. Length = $13\text{ cm}$ and breadth = $12\text{ cm}$.
2. Area = $\text{length} \times \text{breadth} = 13 \times 12 = 156\text{ cm}^2$.

Answer (i): $156\text{ cm}^2$

**Part (ii)**

1. Length = $13\text{ cm}$ and breadth = $10\text{ cm}$.
2. Area = $13 \times 10 = 130\text{ cm}^2$.

Answer (ii): $130\text{ cm}^2$

**Part (iii)**

1. Length = $13\text{ cm}$ and breadth = $8\text{ cm}$. Area = $13 \times 8 = 104\text{ cm}^2$.
2. If breadth is $x\text{ cm}$, the linear pattern representing the area is $13x$.

Answer (iii): $104\text{ cm}^2$, linear pattern: $13x$

**Answer:** The areas are $156\text{ cm}^2$, $130\text{ cm}^2$, and $104\text{ cm}^2$, and the linear pattern is $13x$.

> Common mistake: Using perimeter formula instead of area.

### Question 4

*3 marks · Short answer*

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.

**Part (i)**

1. Length = $7\text{ cm}$, breadth = $11\text{ cm}$, and height = $5\text{ cm}$.
2. Volume = $\text{length} \times \text{breadth} \times \text{height} = 7 \times 11 \times 5 = 385\text{ cm}^3$.

Answer (i): $385\text{ cm}^3$

**Part (ii)**

1. Length = $7\text{ cm}$, breadth = $11\text{ cm}$, and height = $9\text{ cm}$.
2. Volume = $7 \times 11 \times 9 = 693\text{ cm}^3$.

Answer (ii): $693\text{ cm}^3$

**Part (iii)**

1. Length = $7\text{ cm}$, breadth = $11\text{ cm}$, and height = $13\text{ cm}$. Volume = $7 \times 11 \times 13 = 1001\text{ cm}^3$.
2. If height is $h\text{ cm}$, the linear pattern representing the volume is $77h$.

Answer (iii): $1001\text{ cm}^3$, linear pattern: $77h$

**Answer:** The volumes are $385\text{ cm}^3$, $693\text{ cm}^3$, and $1001\text{ cm}^3$, and the linear pattern is $77h$.

> Common mistake: Multiplying only two dimensions or adding them.

### Question 5

*3 marks · Short answer*

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**

1. Total pages in the book = 500.
2. Pages read per day = 20, so after 15 days, total pages read = $20 \times 15 = 300$.
3. Pages left after 15 days = $500 - 300 = 200$.
4. If $d$ represents the number of days, the linear pattern for the pages left is $500 - 20d$.

**Answer:** 200 pages will be left, expressed as the linear pattern $500 - 20d$.

> Common mistake: Adding the read pages to the total instead of subtracting.

## Related pages

- [All Chapter 2 NCERT solutions](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions)
- [Exercise 2.1](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-1)
- [Exercise 2.2](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-2)
- [Exercise 2.4](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-4)
- [Exercise 2.5](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-5)
- [Exercise 2.6](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-6)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student