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Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables with competency-based MCQs, real-life word problems, detailed solutions, shortcut tricks, and board exam insights based on the latest NCERT syllabus.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Pair of Linear Equations in Two Variables
Question Type: Competency-Based MCQs
Difficulty Level: Board Exam Level
Method Covered: Real-Life Applications
Based On: NCERT Latest Syllabus
Introduction:
Linear equations are not limited to classroom exercises. They are widely used in daily life to solve problems involving money, age, distance, shopping, transportation, and business calculations. In competency-based questions, students are expected to understand the situation, form equations correctly, and then solve them using suitable algebraic methods.
The latest CBSE examination pattern focuses on concept application rather than direct formula-based questions. Therefore, practicing real-life situations is essential for scoring high marks.
This practice set contains practical questions that help students connect mathematics with everyday life while strengthening their problem-solving skills.
What You Will Learn?
✔ Forming Linear Equations
✔ Solving Real-Life Problems
✔ Understanding Mathematical Models
✔ Logical Thinking
✔ Board Competency Questions
✔ Application of Algebra
Why This Topic Is Important?
Competency-based questions test understanding rather than memorization and are increasingly common in CBSE Board examinations.
Exam Relevance
✔ CBSE Board Exams
✔ State Board Exams
✔ School Assessments
✔ Competency-Based Tests
✔ Scholarship Exams
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Q1. The sum of two numbers is
$$18$$
and their difference is
$$4$$
The numbers are:
A) $$(11,\ 7)$$
B) $$(10,\ 8)$$
C) $$(12,\ 6)$$
D) $$(13,\ 5)$$
Answer:
$$(11,\ 7)$$
Useful Formula for this Question:
Let the numbers be
$$x$$
and
$$y$$
Then,
$$x+y=18$$
$$x-y=4$$
Concept Behind This Question:
Convert the statement into two linear equations.
Solution:
Adding both equations,
$$2x=22$$
$$x=11$$
Substituting into
$$x+y=18$$
$$11+y=18$$
$$y=7$$
Therefore, the numbers are
$$(11,\ 7)$$
Shortcut / Smart Trick
For “sum” and “difference” problems, elimination is usually the quickest method.
Board Exam Insight
Questions based on sum and difference are frequently asked in board examinations.
Exam Tip:
Always identify keywords like “sum” and “difference” before forming equations.
————————————————–
Q2. A father is
$$30$$
years older than his son. The sum of their ages is
$$54$$
years. The son’s age is:
A) $$10$$
B) $$12$$
C) $$14$$
D) $$16$$
Answer:
$$12$$
Useful Formula for this Question:
Let son’s age be
$$x$$
Father’s age
$$x+30$$
Concept Behind This Question:
Translate age relationships into equations.
Solution:
$$x+(x+30)=54$$
$$2x=24$$
$$x=12$$
Therefore, the son’s age is
$$12$$
years.
Shortcut / Smart Trick
Represent the younger person’s age first.
Board Exam Insight
Age-based word problems appear regularly in competency-based papers.
Exam Tip:
Read age statements carefully to avoid reversing the relationship.
————————————————–
Q3. Two notebooks and one pen cost
$$₹70$$
One notebook and one pen cost
$$₹40$$
The cost of one notebook is:
A) $$₹20$$
B) $$₹30$$
C) $$₹35$$
D) $$₹40$$
Answer:
$$₹30$$
Useful Formula for this Question:
Let notebook cost be
$$x$$
Pen cost be
$$y$$
Concept Behind This Question:
Form equations from shopping situations.
Solution:
$$2x+y=70$$
$$x+y=40$$
Subtracting,
$$x=30$$
Therefore, one notebook costs
$$₹30$$
Shortcut / Smart Trick
Shopping questions are usually solved quickly using elimination.
Board Exam Insight
Cost-based questions are common competency-based problems.
Exam Tip:
Always assign variables before writing equations.
————————————————–
Q4. A taxi charges a fixed amount plus distance charges. If the total fare for one ride is represented using a pair of linear equations, which mathematical topic is mainly used?
A) Quadratic Equations
B) Pair of Linear Equations in Two Variables
C) Probability
D) Trigonometry
Answer:
$$\text{Pair of Linear Equations in Two Variables}$$
Useful Formula for this Question:
Real-life situations can often be modeled using two linear equations.
Concept Behind This Question:
Many pricing systems follow linear relationships.
Solution:
Taxi fare problems involving fixed charges and variable charges can be represented using two linear equations.
Therefore, the correct answer is:
$$\text{Pair of Linear Equations in Two Variables}$$
Shortcut / Smart Trick
Whenever two unknown quantities are involved, think about linear equations.
Board Exam Insight
Conceptual competency questions are becoming more common.
Exam Tip:
Understand the situation before looking for formulas.
————————————————–
Q5. Which of the following situations can be solved using a pair of linear equations in two variables?
A) Finding the area of a circle
B) Finding the probability of an event
C) Determining the prices of two different items from total bills
D) Finding the volume of a cube
Answer:
$$\text{Determining the prices of two different items from total bills}$$
Useful Formula for this Question:
Unknown quantities are represented using variables.
Concept Behind This Question:
Linear equations help determine two unknown values.
Solution:
When two different item prices are unknown and two bills are given, we form two linear equations.
Hence, the correct answer is:
$$\text{Determining the prices of two different items from total bills}$$
Shortcut / Smart Trick
Whenever there are two unknown quantities and two conditions, think of a pair of linear equations.
Board Exam Insight
Application-based conceptual questions are important in the latest CBSE pattern.
Exam Tip:
Identify the unknown quantities before choosing the solving method.
————————————————–
Important Formulas and Concepts
General Form:
$$a_1x+b_1y+c_1=0$$
$$a_2x+b_2y+c_2=0$$
Real-life applications include:
✔ Age Problems
✔ Shopping Problems
✔ Distance Problems
✔ Business Problems
✔ Transportation Problems
————————————————–
FAQs
Q. Why are word problems important?
Answer:
They help apply mathematical concepts to real-life situations.
Q. Which method is best for solving word problems?
Answer:
It depends on the equations formed. Substitution or elimination is commonly used.
Q. How can I avoid mistakes in word problems?
Answer:
Read the question carefully, define variables clearly, and verify the final answer.
————————————————–
Common Mistakes Students Make
❌ Defining variables incorrectly.
❌ Forming wrong equations.
❌ Ignoring units such as years or rupees.
❌ Choosing the wrong solving method.
❌ Not verifying the final answer.
————————————————–
Quick Revision Notes
✔ Read the statement carefully.
✔ Define variables.
✔ Form two equations.
✔ Solve using a suitable method.
✔ Verify the answer.
✔ Mention the unit in the final answer.
————————————————–
Conclusion:
These competency-based MCQs help students understand how pair of linear equations are applied in real-life situations. Regular practice improves logical reasoning, problem-solving ability, and confidence for the latest CBSE Board examination pattern.
Related links
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-8
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-7
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-6
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-5
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-4
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two variables part-3
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-2
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables – Part 1
- Class 10 Maths Chapter 2 Polynomials (Graphical Zeroes) – Part 13
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
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