---
title: "NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2"
url: https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-2
dateModified: 2026-10-07T15:41:27+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2

Chapter 2: Introduction to Linear Polynomials. Every question from Exercise 2.2, with full working and the final answer.

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## Exercise Set 2.2

### Question 1

*3 marks · Short answer*

Find the value of the linear polynomial $5x – 3$ if:
(i) $x = 0$
(ii) $x = –1$
(iii) $x = 2$

**Part (i)**

1. Substitute $x = 0$ in the polynomial $5x - 3$.
2. We get $5(0) - 3 = 0 - 3 = -3$.

Answer (i): $-3$

**Part (ii)**

1. Substitute $x = -1$ in the polynomial $5x - 3$.
2. We get $5(-1) - 3 = -5 - 3 = -8$.

Answer (ii): $-8$

**Part (iii)**

1. Substitute $x = 2$ in the polynomial $5x - 3$.
2. We get $5(2) - 3 = 10 - 3 = 7$.

Answer (iii): $7$

**Answer:** (i) $-3$, (ii) $-8$, (iii) $7$

> Common mistake: Making sign errors while substituting negative values for $x$.

### Question 2

*3 marks · Short answer*

Find the value of the quadratic polynomial $7s^2 – 4s + 6$ if:
(i) $s = 0$
(ii) $s = –3$
(iii) $s = 4$

**Part (i)**

1. Substitute $s = 0$ in the polynomial $7s^2 - 4s + 6$.
2. $7(0)^2 - 4(0) + 6 = 0 - 0 + 6 = 6$

Answer (i): $6$

**Part (ii)**

1. Substitute $s = -3$ in the polynomial $7s^2 - 4s + 6$.
2. $7(-3)^2 - 4(-3) + 6 = 7(9) + 12 + 6 = 63 + 12 + 6 = 81$

Answer (ii): $81$

**Part (iii)**

1. Substitute $s = 4$ in the polynomial $7s^2 - 4s + 6$.
2. $7(4)^2 - 4(4) + 6 = 7(16) - 16 + 6 = 112 - 16 + 6 = 102$

Answer (iii): $102$

**Answer:** (i) $6$, (ii) $81$, (iii) $102$

> Common mistake: Sign errors while substituting negative numbers, such as writing $(-3)^2$ as $-9$ instead of $9$.

### Question 3

*3 marks · Short answer*

The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

**Solution**

1. Let Salil's present age be $x$ years.
2. His mother's present age is $3x$ years.
3. After 5 years, Salil's age will be $x + 5$ and his mother's age will be $3x + 5$.
4. According to the question, $(x + 5) + (3x + 5) = 70$.
5. Simplify the equation: $4x + 10 = 70$, which gives $4x = 60$, so $x = 15$.
6. Salil's present age is 15 years and his mother's present age is $3 \times 15 = 45$ years.

**Answer:** Salil's present age is 15 years, and his mother's present age is 45 years.

> Common mistake: Forgetting to add 5 to both ages for the future condition.

### Question 4

*3 marks · Short answer*

The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

**Solution**

1. Let the two positive integers be $2x$ and $5x$ based on the given ratio $2:5$.
2. The difference between the two integers is given as 63, so $5x - 2x = 63$.
3. Simplify the equation: $3x = 63$, which gives $x = 21$.
4. Calculate the first integer: $2 \times 21 = 42$.
5. Calculate the second integer: $5 \times 21 = 105$.

**Answer:** The two integers are 42 and 105.

> Common mistake: Subtracting in the wrong order leading to negative values.

### Question 5

*3 marks · Short answer*

Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?

**Solution**

1. Let the number of five-rupee coins be $x$.
2. The number of two-rupee coins is $3x$.
3. The total value of five-rupee coins is $5x$ and the total value of two-rupee coins is $2 \times 3x = 6x$.
4. The total amount is given as ₹88, so $5x + 6x = 88$.
5. Simplify to get $11x = 88$, which gives $x = 8$.
6. Number of five-rupee coins is 8 and number of two-rupee coins is $3 \times 8 = 24$.

**Answer:** Ruby has 24 two-rupee coins and 8 five-rupee coins.

> Common mistake: Multiplying the coin count incorrectly with their face values.

### Question 6

*3 marks · Short answer*

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

**Solution**

1. Let the length of the shorter piece of the fence be $x$ feet.
2. The length of the longer piece is $4x$ feet.
3. The total length of the fence is 300 feet, so $x + 4x = 300$.
4. Simplify the equation: $5x = 300$, which gives $x = 60$.
5. The shorter piece is 60 feet and the longer piece is $4 \times 60 = 240$ feet.

**Answer:** The two pieces are 60 feet and 240 feet long.

> Common mistake: Confusing which piece is 4 times the other.

### Question 7

*3 marks · Short answer*

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

**Solution**

1. Let the width of the rectangle be $x$ cm.
2. The length of the rectangle is given as $2x + 3$ cm.
3. The perimeter of the rectangle is given by the formula $2(\text{length} + \text{width}) = 24$.
4. Substitute the expressions for length and width into the perimeter formula: $2((2x + 3) + x) = 24$.
5. Simplify the equation: $2(3x + 3) = 24$, which gives $6x + 6 = 24$.
6. Solve for $x$: $6x = 18$, so $x = 3$.
7. Therefore, the width is $3$ cm and the length is $2(3) + 3 = 9$ cm.

**Answer:** Width = $3$ cm, Length = $9$ cm

> Common mistake: Forgetting to multiply the entire sum of length and width by 2 when using the perimeter formula.

## 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 2.3](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-3)
- [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