---
title: "NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2"
url: https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-2
dateModified: 2026-10-07T15:46:03+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2

Chapter 3: The World of Numbers. Every question from Exercise 3.2, with full working and the final answer.

Free PDF (22 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-9/swavid-ncert-solutions-class-9-maths-chapter-3-the-world-of-numbers-521b6f38aa.pdf

## Exercise Set 3.2

### Question 1

*3 marks · Short answer*

The temperature in the high-altitude desert of Ladakh is recorded as $4\text{ }^\circ\text{C}$ at noon. By midnight, it drops by $15\text{ }^\circ\text{C}$. What is the midnight temperature?

**Solution**

1. Given: Initial temperature at noon = $4^\circ\text{C}$, drop in temperature by midnight = $15^\circ\text{C}$.
2. The idea used is subtraction of integers where a drop represents a negative change.
3. Working: $\text{Midnight temperature} = 4 - 15 = -11$.
4. Result: The midnight temperature is $-11^\circ\text{C}$.

**Answer:** $-11^\circ\text{C}$

> Common mistake: Subtracting $4$ from $15$ to get $11^\circ\text{C}$ instead of accounting for the direction below zero.

### Question 2

*3 marks · Short answer*

A spice trader takes a loan (debt) of $₹850$. The next day, he makes a profit (fortune) of $₹1,200$. The following week, he incurs a loss of $₹450$. Write this sequence as an equation using integers and calculate his final financial standing.

**Solution**

1. Loan (debt) of $₹850$ is represented as $-850$.
2. Profit (fortune) of $₹1,200$ is represented as $+1200$, and loss of $₹450$ as $-450$.
3. Equation: $\text{Financial Standing} = -850 + 1200 - 450 = -100$, meaning a net debt of $₹100$.

**Answer:** $-850 + 1200 - 450 = -100$ (Net debt of $₹100$)

> Common mistake: Treating the loan as a positive number.

### Question 3

*3 marks · Short answer*

Calculate the following using Brahmagupta's laws:
(i) $(-12) \times 5$
(ii) $(-8) \times (-7)$
(iii) $0 - (-14)$
(iv) $(-20) \div 4$

**Part (i)**

1. The product of a debt and a fortune is a debt: $(-12) \times 5 = -60$.

Answer (i): $-60$

**Part (ii)**

1. The product of two debts is a fortune: $(-8) \times (-7) = 56$.

Answer (ii): $56$

**Part (iii)**

1. Subtracting a negative number is equivalent to adding its positive counterpart: $0 - (-14) = 0 + 14 = 14$.

Answer (iii): $14$

**Part (iv)**

1. Dividing a negative debt by a positive number results in a debt: $(-20) \div 4 = -5$.

Answer (iv): $-5$

**Answer:** (i) $-60$, (ii) $56$, (iii) $14$, (iv) $-5$

> Common mistake: Mixing up signs in multiplication and subtraction.

### Question 4

*3 marks · Short answer*

Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number (e.g., $10 - (-5) = 15$).

**Solution**

1. Let having a debt of $₹5$ be represented as $-5$.
2. If you have $₹10$ and someone removes (subtracts) your debt of $₹5$ ($\text{i.e., } -(-5)$), your financial standing increases because you no longer owe that money.
3. Thus, removing a debt is equivalent to gaining money, so $10 - (-5) = 10 + 5 = 15$.

**Answer:** Removing a debt of $₹5$ from your account increases your wealth by $₹5$, making $10 - (-5) = 15$.

> Common mistake: Thinking subtraction of a negative always results in a negative number.

## Related pages

- [All Chapter 3 NCERT solutions](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions)
- [Exercise 3.1](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-1)
- [Exercise 3.3](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-3)
- [Exercise 3.4](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-4)
- [Exercise 3.5](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-5)

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