Exercise 1.3 Class 9 Math Solutions [New Book]
Welcome to the complete solutions of exercise 1.3 class 9 math. This post is designed to help you master real-life math problems using basic algebra, geometry, and arithmetic. You’ll find detailed solutions that show how to handle radical expressions, simplify them, and apply them in practical situations like calculating areas, lengths, and solving financial word problems. These types of problems connect math with daily life, making learning both meaningful and useful.
In addition to step-by-step solutions, this post includes downloadable PDF notes, key definitions, important formulas, and video explanations. You’ll also get help with converting temperatures between Celsius and Fahrenheit, and solving real-world scenarios related to profit, loss, tax, and markup — skills useful in daily life such as shopping, banking, or managing a small business.
Everything is neatly organized for easy access. By going through this post, you’ll not only complete your homework with confidence but also strengthen your problem-solving skills for subjects like physics, chemistry, and economics. Let’s begin and make Exercise 1.3 easier to understand and apply!
Table of Contents
Download/View PDF Notes
What Students Will Learn
- Solve algebraic equations involving consecutive integers and real-world scenarios.
- Work with radical expressions in geometric contexts (e.g., area and length calculations).
- Convert temperatures between Celsius and Fahrenheit scales.
- Calculate profit/loss percentages, tax amounts, and compound markup.
- Apply formulas to solve practical financial and scientific problems.
Exercise 1.1 Class 9 Math
Exercise 1.2 Class 9 Math
TextBook of Class 9 Mathematics
Common Mistakes to Avoid
1.Consecutive Integers: Confusing consecutive integers (e.g., 5, 6) with consecutive even or odd integers (e.g., 4, 6).
2.Radical Simplification: Mishandling operations like
(a + b)(c + d)
when working with surds.
3.Temperature Conversion: Using the formula
F = (9/5) × C + 32 incorrectly by adding 32 before multiplying.
4.Profit Percentage: Dividing profit by selling price instead of cost price.
5.Tax Calculation: Applying the tax rate to total income instead of taxable income.
6.Compound Markup: Forgetting to include the principal amount when calculating total amount.
Solved Problems
Problem 1:
Question: Find two numbers whose sum is 68 and difference is 22.
Solution:
Let the numbers be x and y.
x + y = 68 (1)
x − y = 22 (2)
Add equations (1) and (2):
2x = 90 ⇒ x = 45
Substitute into (1):
45 + y = 68 ⇒ y = 23
Answer: 45 and 23
Problem 2:
Question: Convert 48°C to Fahrenheit.
Solution:
Use the formula:
F = (9/5) × 48 + 32 = 86.4 + 32 = 118.4°F
Answer: 118.4°F
Key Definitions
Consecutive Integers: Numbers that follow each other without gaps (e.g., 13, 14, 15).
Profit Percentage: The profit percentage is the profit expressed as a percentage of the cost price. It is calculated using the formula:
Profit % = (Profit / Cost Price) × 100 %
Taxable Income: The income amount after removing the exempted amount.
Compound Markup: Interest calculated on the initial principal and on previously added interest.
Important Formulas
Temperature Conversion:
F = (9/5) × C + 32
Profit Percentage:
Profit % = ((SP − CP) / CP) × 100
Tax Calculation:
Tax = Taxable Income × (Rate / 100)
Compound Markup (Annual):
A = P × (1 + r)ᵗ
where
A = Final Amount,
P = Principal,
r = Rate (as a decimal),
t = Time in years
Real-Life Uses
- Financial Management: Calculating business profit/loss.
- Weather Forecasting: Converting temperatures for global reports.
- Engineering & Architecture: Using surds in construction design and calculations.
- Taxation: Computing income tax on salaried earnings.
- Banking: Calculating compound interest and markup on savings or loans.
Short Answer Questions
Q: What are consecutive integers?
A: Numbers that follow one after another without any gap, e.g., 7, 8, 9.
Q: Simplify 3 × √12
A: 3 × √12 = 3 × 2√3 = 6√3
Q: What is the Fahrenheit equivalent of 0°C?
A: F = (9/5) × 0 + 32 = 32°F
Q: Find the profit percentage if CP = 200 and SP = 250
A: Profit =SP – CP
So Profit= 50, Profit % = (Profit / CP) × 100
Profit % = (50 / 200) × 100 = 25%
Q: Simplify (2 + 3√2)(5 − 2√2) and express in form a + b√2
A:
\((2 + 3\sqrt{2})(5 – 2\sqrt{2}) = 10 + 15\sqrt{2} – 4\sqrt{2} – 12\)
\( -2 + 11\sqrt{2}\)
Answer: \(-2 + 11\sqrt{2}\)
Q: What is the compound markup on Rs. 1000 at 10% for 1 year?
A:
A = 1000 × (1 + 0.10)¹ = 1100
Compound markup = 1100 − 1000 = Rs. 100.