NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.3 | 2026-27

Think and Reflect 

1. Predict the number of squares in the next three stages of the pattern and write the sequence of numbers up to Stage 7 of the pattern. 

Solution

Practice on Your Own

Think and Reflect 

1. Using the expression 2n – 1, can you find out how many tiles will be there in the 15th stage and the 26th stage of the pattern? Also, which stage will contain 21 tiles and 47 tiles? 

Solution:

For the 15th stage:

Number of tiles = 2(15) – 1 

             = 30 – 1 

 = 29

Therefore, the 15th stage will have 29 tiles.

For the 26th stage:
Number of tiles = 2(26) – 1 

  = 52 – 1 

  = 51

Therefore, the 26th stage will have 51 tiles.

For 21 tiles:
2n – 1 = 21

⇒ 2n   = 22
⇒ n     = 11

Therefore, 21 tiles is the 11th stage.

For 47 tiles:

We solve the equation:
2n – 1 = 47

  ⇒ 2n = 48
    ⇒ n = 24

Therefore, 47 tiles is the 24th stage.

Think and Reflect 

1. What amount will be left on the 15th day? How many days will it take for the entire amount to be spent?

Solution:
The amount left on the nth day is given by ₹(100 – 5n).

Therefore, on the 15th day, the amount left will be:
₹(100 – 5 × 15) = ₹25

Hence, the amount left on the 15th day will be ₹25.

Since ₹5 is spent each day, the number of days required to spend the entire amount is:

100 ÷ 5 = 20 days

Therefore, it will take 20 days to spend the entire amount.

Think and Reflect 

1. For how many km will the fare be ₹ 130?

Solution:

The expression representing the fare is 15n – 5, where n represents the number of kilometres and n > 2.

According to the question:
15n – 5 = 130

⇒ 15n = 135

⇒ n = 9

Hence, for 9 km, the fare will be ₹130.

Exercise Set 2.3 

Solve the following: 

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 account = ₹500

Pocket money received every month = ₹150

The amount after n months = 500 + 150n

Therefore, the linear expression representing the amount in the nth month is:

₹(500 + 150n)

For the second month:

500 + 150(2) = 500 + 300 = ₹800

Hence, the student will have ₹800 at the end of the second month.

The amount will increase by ₹150 every month, and the linear expression for the amount in the nth month is ₹(500 + 150n), where n is the number of months.

2. A rally starts with 120 members. Each hour, 9 members leave the group. How many members 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 members = 120

Number of members leaving every hour = 9

After 1 hour:
Number of members = 120 – 9(1) = 111

After 2 hours:
Number of members = 120 – 9(2) = 102

After 3 hours:
Number of members = 120 – 9(3) = 93

Therefore, the number of members after 1, 2, 3, … hours will be 111, 102, 93, …

The linear expression representing the number of members at the end of the nth hour is:

120 – 9n

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 the rectangle = 13 cm

Area of rectangle = Length × Breadth

(i) When breadth = 12 cm:
Area = 13 × 12 = 156 cm²

(ii) When breadth = 10 cm:
Area = 13 × 10 = 130 cm²

(iii) When breadth = 8 cm:
Area = 13 × 8 = 104 cm²

Therefore, the areas of the rectangles are 156 cm², 130 cm², and 104

4. Suppose the length of a rectangular box is 7 cm and the 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 the rectangular box = 7 cm
Breadth of the rectangular box = 11 cm

Volume of the rectangular box = Length × Breadth × Height

(i) When height = 5 cm:
Volume = 7 × 11 × 5 = 385 cm³

(ii) When height = 9 cm:
Volume = 7 × 11 × 9 = 693 cm³

(iii) When height = 13 cm:
Volume = 7 × 11 × 13 = 1001 cm³

Therefore, the volumes of the rectangular box are 385 cm³, 693 cm³, and 1001 cm³.

The linear expression representing the volume V(h) in terms of the height h is:

V(h) = 77h, where h is the height of the rectangular box. 

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 pages in the book = 500

Number of pages read per day = 20

The number of pages left after n days can be represented as:

L(n) = 500 – 20n

For n = 15 days:

L(15) = 500 – 20(15)

= 500 – 300

= 200

Therefore, after 15 days, 200 pages of the book will be left to read.

The linear pattern representing the pages left is:

500, 480, 460, 440, …

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Using Class 9 Maths NCERT Solutions Chapter 2 Exercise 2.3 helps students learn the correct problem-solving techniques and understand how to approach different types of questions from the exercise. The solutions also help students check their answers and improve their accuracy.

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• Helps in understanding important concepts of Linear Polynomials

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Students can also use Class 9 Maths Chapter 2 Solutions Exercise 2.3 to practise regularly and strengthen their understanding through clear, easy-to-follow solutions.

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