Last Updated on April 2, 2025 by XAM CONTENT
Hello students, we are providing case study questions for class 10 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 10 maths. In this article, you will find case study questions for CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables. It is a part of Case Study Questions for CBSE Class 10 Maths Series.
| Chapter | Pair of Linear Equations in Two Variables |
| Type of Questions | Case Study Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Unit | Unit 2 Algebra |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Case Study |
Case Study Questions on Pair of Linear Equations in Two Variables
Questions
Passage 1:
A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is ₹ 9000 and from batch II is ₹ 26000 . Assume that each poor child pays ₹ $x$ per month and each rich child pays ₹ $y$ per month.
Based on the given information, solve the following questions:
Q. 1. Represent the information given above in terms of x and y.
Q. 2. Find the monthly fee paid by a poor child.
Or
Find the difference in the monthly fee paid by a poor child and a rich child.
Q. 3. If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?
Answers
1. Given that, each poor child pays ₹ $x$ per month and each rich child pays ₹ y per month.
First Condition: In batch I, there are 20 poor and 5 rich children. The total monthly collection of fees from batch I is ₹ 9000 .
i.e.,
$$
20 x+5 y=9000 (1)
$$
Second Condition: In batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch II is ₹26000. i.e.,
$$
5 x+25 y=26000 (2)
$$
2.
\[
\begin{aligned}
& \text{Multiplying eq. (1) by 5 and subtracting from eq. (2):} \\
& (5x + 25y) – 5(20x + 5y) = 26000 – 5 \times 9000 \\
\Rightarrow & 5x + 25y – 100x – 25y = 26000 – 45000 \\
\Rightarrow & -95x = -19000 \\
\Rightarrow & x = \frac{-19000}{-95} = 200
\end{aligned}
\]
OR
\[
\text{Multiplying eq. (2) by 4 and subtracting from eq. (1), we get:}
\]
\[
\begin{aligned}
& (20x + 5y) – 4(5x + 25y) = 9000 – 4 \times 26000 \\
\Rightarrow & 20x + 5y – 20x – 100y = 9000 – 104000 \\
\Rightarrow & -95y = -95000 \\
\Rightarrow & y = \frac{-95000}{-95} = 1000
\end{aligned}
\]
\[
\therefore \text{Monthly fee paid by a rich child is ₹1000.}
\]
\[
\text{Putting the value of } y \text{ in eq. (1), we get:}
\]
\[
\begin{aligned}
& 20x + 5 \times 1000 = 9000 \\
\Rightarrow & 20x = 9000 – 5000 = 4000 \\
\Rightarrow & x = \frac{4000}{20} = 200
\end{aligned}
\]
Monthly fee paid by a poor child is ₹200.
The difference in the monthly fee is ₹ (1000 – 200) = ₹800.
3. Given that, there are 10 poor and 20 rich children in batch $11=10 x+20 y$.
$\therefore$ Total monthly collection of fees from batch II
= 10 × 200 + 20 × 1000
= 2000 + 20000
= ₹22000
Passage 2:
A seller sold 40 books comprising novels and storybooks. Novels cost ₹250 each and storybooks cost ₹150 each. He collected ₹8,500 in total.
Q1. Form two linear equations in x and y (number of novels and storybooks).
Difficulty Level: Medium
Ans. Here is the equations:
- x + y = 40
- 250x + 150y = 8500
Q2. Eliminate y to solve for x.
Difficulty Level: Medium
Ans. Multiply first equation by 150 and subtract:
150x + 150y = 6000
(250x + 150y) – (150x + 150y) = 8500 – 6000
⇒ 100x = 2500 ⇒ x = 25
Q3. Find number of storybooks.
Difficulty Level: Easy
Ans. y = 40 – 25 = 15
Q4. What amount was collected from novels?
Difficulty Level: Medium
Ans. 25 × ₹250 = ₹6,250
Also check
- Arithmetic Progressions Class 10 Case Study Questions Maths Chapter 5
- Quadratic Equations Class 10 Case Study Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Case Study Questions Maths Chapter 3
- Polynomials Class 10 Case Study Questions Maths Chapter 2
- Real Numbers Class 10 Case Study Questions Maths Chapter 1
🚀 Boost Your Exam Prep: Get case study questions for all subjects (Class 6-12) now!
Topics from which case study questions may be asked
- Pair of Linear Equations in Two Variables
- Graphical Method of Solution
- Consistency and Inconsistency
- Algebraic Conditions for Number of Solutions
- Algebraic Solution Methods
- Substitution Method
- Elimination Method
- Simple Situational Problems
Case study questions based on above topics may be asked.
Frequently Asked Questions (FAQs) on Pair of Linear Equations in Two Variables Case Study
Q1: What are case study questions in Chapter 3 – Pair of Linear Equations?
A1: Case study questions are real-life application-based problems where students are given a scenario involving two related quantities. They must form and solve two linear equations using methods like substitution, elimination, or cross-multiplication.
Q2: Which concepts from this chapter are important for case-based questions?
A2: Key concepts include:
Forming linear equations from a word problem
Graphical interpretation of two-variable equations
Solving equations by substitution, elimination, and cross-multiplication
Understanding consistency and types of solutions (unique, infinite, no solution)
Q3: How do I identify variables in a case study question?
A3: Read the scenario carefully and identify two unknowns (like age, cost, speed, number of items, etc.). Assign letters (e.g., x and y), then frame equations based on the conditions given.
Q4: What type of real-life problems can appear in these questions?
A4: Common situations include:
Ticket pricing for adults and children
Speed and distance of vehicles
Cost and quantity of two items
Age-related word problems
Time-based work problems
Q5: How are case study questions marked in the CBSE exam?
A5: A case study question typically carries 4 marks, divided into 4 sub-questions (mostly MCQs or short one-liners). You must understand the scenario and apply the right method to solve each.
Q6: Which method is best for solving a case study problem quickly?
A6: If equations are simple, use substitution or elimination. For equations with neatly balanced coefficients, cross-multiplication works well. Choose the method that requires the least calculation based on the question.
Q7: Are there any online resources or tools available for practicing “Pair of Linear Equations in Two Variables” case study questions?
A7: We provide case study questions for CBSE Class 10 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.
Q8: Can graphical questions be part of case study sets?
A8: Yes. You may be asked to interpret a graph showing two linear equations to determine whether they intersect, are parallel, or coincide — indicating unique, no, or infinite solutions respectively.
Q9: What are some tips to solve these questions accurately?
A9: Clearly define the variables
Translate the conditions into algebraic equations
Choose the solving method wisely
Recheck by substituting the values into both equations
Q10: Are case study questions different from HOTS questions?
A10: Yes. Case study questions are contextual and application-based, often real-world in nature. HOTS (Higher Order Thinking Skills) questions test deeper reasoning and may not always involve real-life scenarios.
