---
title: "NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.5"
url: https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-5
dateModified: 2026-10-07T15:41:27+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.5

Chapter 2: Introduction to Linear Polynomials. Every question from Exercise 2.5, 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 2.5

### Question 1

*3 marks · Short answer*

A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was ₹400. When she accessed 14 modules, her bill was ₹500. If the monthly bill $y$ depends on the number of modules accessed, $x$, according to the relation $y = ax + b$, find the values of $a$ and $b$.

**Solution**

1. We are given the linear relation $y = ax + b$.
2. When $x = 10$, $y = 400$, so $400 = 10a + b$.
3. When $x = 14$, $y = 500$, so $500 = 14a + b$.
4. From the first equation, $b = 400 - 10a$. Substituting this in the second equation gives $500 = 14a + (400 - 10a)$, which simplifies to $100 = 4a$, so $a = 25$.
5. Substituting $a = 25$ gives $b = 400 - 10(25) = 150$.
6. Thus, $a = 25$ and $b = 150$.

**Answer:** $a = 25$ and $b = 150$

> Common mistake: Errors in simultaneous linear equations substitution or signs.

### Question 2

*3 marks · Short answer*

A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student using the gym observed that when she used the badminton court for 10 hours, her bill was ₹800. When she used it for 15 hours, her bill was ₹1100. If the monthly bill $y$ depends on the hours of the use of the badminton court, $x$, according to the relation $y = ax + b$, find the values of $a$ and $b$.

**Solution**

1. We are given the linear relation $y = ax + b$.
2. When $x = 10$, $y = 800$, so $800 = 10a + b$.
3. When $x = 15$, $y = 1100$, so $1100 = 15a + b$.
4. From the first equation, $b = 800 - 10a$. Substituting this into the second equation gives $1100 = 15a + (800 - 10a)$, which yields $300 = 5a$, so $a = 60$.
5. Substituting $a = 60$ gives $b = 800 - 10(60) = 200$.
6. Thus, $a = 60$ and $b = 200$.

**Answer:** $a = 60$ and $b = 200$

> Common mistake: Wrong assignment of variables $x$ and $y$.

### Question 3

*3 marks · Short answer*

Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F), which is given by °C = $a$ °F + $b$. Find $a$ and $b$, given that ice melts at 0 degrees Celsius and 32 degrees Fahrenheit, and water boils at 100 degrees Celsius and 212 degrees Fahrenheit.
(Hint: When °C = 0, °F = 32 and when °C = 100, °F = 212. Use this information to find $a$ and $b$, and thus, the linear relationship between °C and °F.)

**Solution**

1. We are given the linear relation $\text{\textdegree}C = a \text{\textdegree}F + b$.
2. When $\text{\textdegree}C = 0$, $\text{\textdegree}F = 32$, so $0 = 32a + b$.
3. When $\text{\textdegree}C = 100$, $\text{\textdegree}F = 212$, so $100 = 212a + b$.
4. From the first equation, $b = -32a$. Substituting this into the second equation gives $100 = 212a - 32a$, which simplifies to $100 = 180a$, so $a = \frac{100}{180} = \frac{5}{9}$.
5. Substituting $a = \frac{5}{9}$ gives $b = -32 \left(\frac{5}{9}\right) = -\frac{160}{9}$.
6. Thus, $a = \frac{5}{9}$ and $b = -\frac{160}{9}$.

**Answer:** $a = \frac{5}{9}$ and $b = -\frac{160}{9}$

> Common mistake: Confusing the independent and dependent variables as specified in the relation.

## 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 2.3](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 2.6](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