ROUTERA


Chapter 5 Arithmetic Progressions

Class 10th Maths Chapter Case Study Questions


Case Study 1: Savings Plan for College

Case Description:
Ravi, a high school student, is planning to save money for his college education. He decides to save a fixed amount every month and gradually increase his savings as he progresses through high school. He starts by saving ₹500 in the first month and increases his savings by ₹100 each month. He wants to find out how much he will save in total by the end of 12 months, the amount he will save in the last month, and other related aspects of his savings plan. Ravi's monthly savings form an arithmetic progression where the first term a=500a = 500 and the common difference d=100d = 100.

MCQs:

  1. How much will Ravi save in the 12th month?

    • A) ₹1,700
    • B) ₹1,800
    • C) ₹2,000
    • D) ₹2,200
  2. What will be the total amount Ravi saves by the end of 12 months?

    • A) ₹12,000
    • B) ₹9,600
    • C) ₹14,400
    • D) ₹18,000
  3. How many months will it take for Ravi to save exactly ₹2,000 in one month?

    • A) 13 months
    • B) 15 months
    • C) 16 months
    • D) 12 months
  4. If Ravi continues this savings plan for 24 months, what will be his total savings at the end of 24 months?

    • A) ₹39,600
    • B) ₹28,800
    • C) ₹45,600
    • D) ₹32,400

Case Study 2: Fitness Training Program

Case Description:
A fitness trainer has designed a running program for his trainee, Suresh, to gradually build his stamina over a 10-week period. In the first week, Suresh runs 2 kilometers per day. Each subsequent week, the trainer increases the daily distance by 0.5 kilometers. This daily distance forms an arithmetic progression. Suresh wants to know the distance he will be running daily by the end of 10 weeks, the total distance he will run in the 10th week, and the total kilometers covered by the end of the 10-week program.

MCQs:

  1. How many kilometers will Suresh run daily by the 10th week?

    • A) 5.5 km
    • B) 7 km
    • C) 6.5 km
    • D) 7.5 km
  2. How much distance will Suresh run in total in the 10th week (7 days)?

    • A) 45.5 km
    • B) 49 km
    • C) 52.5 km
    • D) 42 km
  3. What is the total distance Suresh runs over the entire 10-week period?

    • A) 210 km
    • B) 240 km
    • C) 280 km
    • D) 315 km
  4. In which week will Suresh be running 8 kilometers per day?

    • A) 13th week
    • B) 15th week
    • C) 12th week
    • D) 14th week

Case Study 3: Book Reading Challenge

Case Description:
Sima loves reading and challenges herself to read more books each month. She starts by reading 2 books in the first month and sets a goal to read 2 additional books each subsequent month compared to the previous month. This reading challenge forms an arithmetic progression with the first term a=2a = 2 and the common difference d=2d = 2. Sima aims to track the total number of books read over a year, the number of books read in the 12th month, and if she can read at least 100 books in a year.

MCQs:

  1. How many books will Sima read in the 12th month?

    • A) 20 books
    • B) 24 books
    • C) 22 books
    • D) 26 books
  2. What will be the total number of books Sima reads over 12 months?

    • A) 168 books
    • B) 144 books
    • C) 156 books
    • D) 132 books
  3. In which month will Sima read exactly 16 books?

    • A) 8th month
    • B) 7th month
    • C) 9th month
    • D) 10th month
  4. If Sima wants to read at least 100 books in 10 months, by how many books does her reading plan exceed her goal?

    • A) 20 books
    • B) 25 books
    • C) 30 books
    • D) 15 books

Case Study 4: Fundraising Marathon

Case Description:
A school organizes a fundraising marathon in which participants pay an entry fee that increases each year to support a local charity. In the first year, the entry fee is ₹500, and each subsequent year, the entry fee is raised by ₹100. The school wants to estimate the entry fee for the 10th year, the total amount collected from one participant over 10 years, and the total collection if 200 participants join each year.

MCQs:

  1. What will be the entry fee in the 10th year?

    • A) ₹1,200
    • B) ₹1,400
    • C) ₹1,500
    • D) ₹1,800
  2. How much will one participant pay in total over the course of 10 years?

    • A) ₹12,500
    • B) ₹10,000
    • C) ₹15,000
    • D) ₹18,000
  3. If 200 participants join each year, what will be the total collection over 10 years?

    • A) ₹2,500,000
    • B) ₹2,000,000
    • C) ₹1,500,000
    • D) ₹3,000,000
  4. In which year will the entry fee first reach ₹2,000?

    • A) 12th year
    • B) 15th year
    • C) 16th year
    • D) 20th year

Case Study 5: Water Usage for Agriculture

Case Description:
A farmer uses a drip irrigation system and plans to gradually increase water usage by a fixed amount each month to accommodate his growing crops. In the first month, he uses 100 liters of water, and he increases his water usage by 20 liters each month. The farmer wants to determine his water usage by the 12th month, the total water used over a year, and how much additional water he would need if he wanted to double the amount used each month after 12 months.

MCQs:

  1. How much water will the farmer use in the 12th month?

    • A) 320 liters
    • B) 340 liters
    • C) 360 liters
    • D) 380 liters
  2. What will be the total water usage over 12 months?

    • A) 2,520 liters
    • B) 3,240 liters
    • C) 2,820 liters
    • D) 3,600 liters
  3. If the farmer decides to double his monthly usage after 12 months, how much water will he use in the 13th month?

    • A) 680 liters
    • B) 640 liters
    • C) 700 liters
    • D) 720 liters
  4. By how much would the farmer's total annual water usage increase if he continued doubling the monthly amount after 12 months for the next 12 months?

    • A) 15,240 liters
    • B) 18,360 liters
    • C) 21,120 liters
    • D) 19,820 liters