Last Updated on September 17, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 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 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 11 Direct and Inverse Proportions. It is a part ofÂ Case Study Questions for CBSE Class 8 MathsÂ Series.

Chapter | Direct and Inverse Proportions |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 8 |

Subject | Maths |

Useful for | Class 8 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 8 Maths Chapterwise Case Study |

### Case Study Questions on Direct and Inverse Proportions

**Questions**

**Passage 1: **

A hotel has 320 rooms and 32 cleaners to maintain them. With full capacity of staff, it took 2 hours to clean all the rooms.

Q. 1. On Monday 20% of the cleaners were not available. Will the cleaning of all rooms take more than 2 hours? How can you say so?

** Difficulty Level: **Easy

Sol. Yes.

As, Number of man required to complete work is inversely proportional to time taken by them.

Q. 2. Ishan says, “The number cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms.”

Mira says, “The number of cleaners available in the hotel is inversely proportional to the time taken by them to clean the rooms.”

Who is correct? Give reason.

** Difficulty Level: **Medium

Sol. Mira is correct,

As Number of cleaners are inversely proportional to time taken

Q. 3. Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?

** Difficulty Level: **Easy

Sol. Number of rooms = 320

Number of cleaners = 32

Number of rooms cleaned by each cleaner = 320 / 32 = 10

Q. 4. The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?

** Difficulty Level: **Easy

Ans. Option (b) is correct.

Explanation: Number of cleaners = 40 (32 + 8)

Number of rooms cleaned by each cleaner = 320 / 40 = 8

So, Number of rooms decreased by (10 â€“ 8) = 2

Q. 5. How many rooms has to be cleaned in an hour by each cleaner after the increase in the number of staff? (

(a) 1

(b) 4

(c) 8

(d) 10

** Difficulty Level: **Easy

Ans. Option (b) is correct.

Explanation: Number of rooms to be cleaned in 2 hours = 8

Number of rooms to be cleaned in 1 hour = 8/2 = 4

### Also check

- Direct and Inverse Proportions Class 8 Case Study Questions Maths Chapter 11
- Exponents and Powers Class 8 Case Study Questions Maths Chapter 10
- MensurationÂ Class 8 Case Study Questions Maths Chapter 9
- Algebraic Expressions and IdentitiesÂ Class 8 Case Study Questions Maths Chapter 8
- Comparing QuantitiesÂ Class 8 Case Study Questions Maths Chapter 7
- Cube and Cube RootsÂ Class 8 Case Study Questions Maths Chapter 6
- Square and Square RootsÂ Class 8 Case Study Questions Maths Chapter 5
- Data HandlingÂ Class 8 Case Study Questions Maths Chapter 4
- Understanding QuadrilateralsÂ Class 8 Case Study Questions Maths Chapter 3
- Linear Equations in One VariableÂ Class 8 Case Study Questions Maths Chapter 2
- Rational NumbersÂ Class 8 Case Study Questions Maths Chapter 1

### Download eBooks for CBSE Class 8 Maths

- Rational Numbers Topicwise Worksheet for CBSE Class 8 Maths
- Linear Equations in One Variable Worksheet for CBSE Class 8 Maths
- Understanding Quadrilaterals Worksheet for CBSE Class 8 Maths
- Data Handling Worksheet for CBSE Class 8 Maths
- Squares and Square Roots Worksheet for CBSE Class 8 Maths
- Cube and Cube Roots Worksheet for CBSE Class 8 Maths
- Comparing Quantities Worksheet for CBSE Class 8 Maths
- Algebraic Expressions and Identities Worksheet for CBSE Class 8 Maths

### Topics from which case study questions may be asked

- Direct Proportions
- Inverse Proportion

Whenever two quantities have a relation with each other such that if one changes, the other also changes then these quantities are said to be inter related with each other. This is called variation.

Example: (a) If number of something purchased increases then cost also increases.

(b) If speed of vehicle increases, time taken decreases.

Quantities increasing or decreasing together need not be in direct proportion or indirect proportion.

Case study questions from the above given topic may be asked.

### Frequently Asked Questions (FAQs) on Direct and Inverse Proportions Case Study

#### Q1: What is direct proportion?

A1: Direct proportion refers to a relationship between two quantities where an increase in one quantity leads to a proportional increase in the other, and a decrease in one result in a proportional decrease in the other. Mathematically, two quantities x and y are in direct proportion if x/y=k, where k is a constant.

#### Q2: What is inverse proportion?

A2: Inverse proportion describes a relationship between two quantities where an increase in one quantity leads to a proportional decrease in the other and vice versa. In this case, the product of the two quantities remains constant. Mathematically, two quantities x and y are in inverse proportion if *x* Ã— *y* = k, where k is a constant.

#### Q3: How can I identify if two quantities are in direct proportion?

A3: – To identify if two quantities are in direct proportion, check if their ratio remains constant when they change. If the ratio of the two quantities stays the same, they are in direct proportion. For example, if 4 pencils cost â‚¹20, and 8 pencils cost â‚¹40, the ratio of pencils to price remains constant, indicating direct proportion.

#### Q4: How can I identify if two quantities are in inverse proportion?

A4: To determine if two quantities are in inverse proportion, check if the product of the two quantities remains constant when they change. If multiplying the two quantities always gives the same result, they are in inverse proportion. For example, if 4 workers take 6 days to complete a task, and 8 workers take 3 days, the product of workers and days (4 Ã— 6 = 24 and 8 Ã— 3 = 24) remains constant, indicating inverse proportion.

#### Q5: Can you give a real-life example of direct proportion?

A5: A common real-life example of direct proportion is the relationship between distance and time when speed is constant. If a car travels at a constant speed, doubling the time will double the distance covered, maintaining a constant ratio between distance and time.

#### Q6: **Can you provide an example of inverse proportion in daily life?**

A6: A typical example of inverse proportion is the relationship between the number of workers and the time taken to complete a task. If more workers are assigned to a job, the time required to finish the work decreases proportionally, assuming the work is equally distributed among the workers.

#### Q7: **Why is learning about direct and inverse proportions important?**

A7: Understanding direct and inverse proportions is crucial as these concepts are frequently used in real-life situations, such as calculating speed, cost, work efficiency, and more. Mastery of these concepts helps students develop problem-solving skills and apply mathematical relationships to practical problems.

#### Q8: **Are there any online resources or tools available for practicing Direct and Inverse Proportions** **case study questions?**

A8: We provide case study questions for CBSE Class 8 Maths on ourÂ 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 visitÂ Physics GurukulÂ website. they are having a large collection of case study questions for all classes.