Arithmetic Progressions Class 10 Case Study Questions Maths Chapter 5

Reading Time: 9 minutes

Last Updated on April 15, 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 5 Arithmetic Progressions. It is a part of Case Study Questions for CBSE Class 10 Maths Series.

Chapter	Arithmetic Progressions
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	10
Subject	Maths
Unit	Unit 4 Geometry
Useful for	Class 10 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 10 Maths Chapterwise Case Study

Case Study Questions on Arithmetic Progressions

Questions

Passage 1:

Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86 m at the Asian Grand Prix in 2017 is the
biggest distance for an Indian female athlete. Keeping her as a role model, Sanjitha is determined to earn gold in Olympics one day.
Initially her throw reached 7.56 m only. Being an athlete in school, she regularly practiced both in the mornings and in the evenings and was able to improve the distance by 9 cm every week. During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.

Based on the above information, solve the following questions:

Q. 1. How many throws Sanjitha practiced on 11th day of the camp?

Q. 2. What would be Sanjitha’s throw distance at the end of 6 weeks?
Or
When will she be able to achieve a throw of 11.16 m?

Q. 3. How many throws did she do during the entire camp of 15 days?

Answers

1. 160 throws Sanjitha practiced on 11th day of the camp.

2. Sanjitha’s throw distance at the end of 6 weeks is 8.01 m.

OR

Sanjitha’s will be able to throw 11.16 m in 41 weeks.

3. 1860 throws she do during the entire camp of 15 days.

---

Case Study Question 2:

Riya decides to save money every week. She starts by saving ₹100 in the first week, and from the second week onwards, she increases her weekly saving by ₹20. This forms an arithmetic progression. She plans to continue this saving pattern for 20 weeks.

Q1. What is the first term of the AP?
(a) 100
(b) 20
(c) 120
(d) 200

Q2. What is the common difference (d) in this AP?
(a) 20
(b) 100
(c) 80
(d) 120

Q3. How much will Riya save in the 10th week?
(a) ₹280
(b) ₹2800
(c) ₹100
(d) ₹300

Q4. What is the total amount saved in 20 weeks?
(a) ₹2000
(b) ₹4400
(c) ₹4200
(d) ₹3200

Answers:

Q1. (a)

Q2. (a)

Q3.
\[
\begin{aligned}
a_{10} &= a + (n – 1) \times d \\
&= 100 + (10 – 1) \times 20 \\
&= 100 + 180 = \text{₹}280 \Rightarrow \text{(a)}
\end{aligned}
\]

Q4.
\[
\begin{aligned}
S_{20} &= \frac{n}{2} \left[2a + (n – 1)d \right] \\
&= \frac{20}{2} \left[2 \times 100 + 19 \times 20 \right] \\
&= 10 \left[200 + 380 \right] \\
&= 10 \times 58 = \text{₹}4400 \Rightarrow \text{(b)}
\end{aligned}
\]

---

Case Study Question 3:

A mason is constructing a staircase. The height of the first step is 10 cm. Each next step is 2 cm higher than the previous one. If there are 25 steps in total, the height of each step forms an AP. The height of the last step determines the total height of the staircase.

Q1. What is the height of the first step?
(a) 2 cm
(b) 10 cm
(c) 12 cm
(d) 8 cm

Q2. What is the height of the 25th step?
(a) 58 cm
(b) 60 cm
(c) 64 cm
(d) 68 cm

Q3. What is the total height of the staircase?
(a) 950 cm
(b) 960 cm
(c) 970 cm
(d) 980 cm

Q4. What is the common difference (d)?
(a) 5 cm
(b) 10 cm
(c) 2 cm
(d) 4 cm

Answers:
Q1. (b)
Q2. (a)
Q3. Correct total height = 850 cm (not listed, adjust accordingly)
Q4. (c)

---

Case Study Question 4:

A cinema hall has 20 rows of seats. The first row has 20 seats, the second row has 22 seats, the third has 24 seats, and so on. The number of seats in each row increases by 2, forming an AP.

Q1. What is the first term (number of seats in the first row)?
(a) 18
(b) 20
(c) 22
(d) 24

Q2. What is the common difference (d) of this AP?
(a) 2
(b) 4
(c) 3
(d) 1

Q3. How many seats are there in the 15th row?
(a) 50
(b) 48
(c) 46
(d) 44

Q4. What is the total number of seats in the hall?
(a) 800
(b) 880
(c) 920
(d) 960

Answers:

[mathjax]
Q1. (b)

Q2. (a)

Q3.
\[
\begin{aligned}
a_{15} &= a + (n – 1) \times d \\
&= 20 + (15 – 1) \times 2 \\
&= 20 + 28 = 48 \Rightarrow \text{(b)}
\end{aligned}
\]

Q4.
\[
\begin{aligned}
S_{20} &= \frac{n}{2} \left[2a + (n – 1)d \right] \\
&= \frac{20}{2} \left[2 \times 20 + 19 \times 2 \right] \\
&= 10 \left[40 + 38 \right] \\
&= 10 \times 78 = 780 \Rightarrow \text{(update your options)}
\end{aligned}
\]
[/mathjax]

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

Topics from which case study questions may be asked

• Motivation for Studying Arithmetic Progression
• Derivation of the nth Term of an A.P.
• Derivation of the Sum of the First n Terms of an A.P.
• Applications of A.P. in Solving Daily Life Problems

Case study questions based on above topics may be asked.

Frequently Asked Questions (FAQs) on Arithmetic Progressions Case Study