Class 8 Maths - MAHARASHTRA
Proportional Reasoning-2
Proportional Reasoning-2 builds upon the fundamental concepts of ratio and proportion learned earlier, diving deeper into direct and inverse variation, partnership, and chain rule. In this chapter, Maharashtra Board Class 8 students learn how quantities change in relation to one another—either increasing together at a constant rate or moving in opposite directions. Mastering this chapter is crucial for solving real-life word problems involving time and work, speed and distance, and financial partnerships. These topics carry significant weightage in the MSBSHSE mathematics board examinations, frequently appearing in 3-mark and 4-mark descriptive question sections.
Start Learning FreeKey Concepts
Direct Variation
When two quantities are related such that as one increases, the other also increases at the same constant rate, their ratio remains constant (x/y = k).
Inverse Variation
When two quantities are related such that as one increases, the other decreases at the same constant rate, their product remains constant (x × y = k).
Constant of Variation
The fixed numerical value (denoted by 'k') that relates two variables in direct or inverse proportion.
Partnership
A business arrangement where profit or loss is shared among partners in proportion to the capital invested and the time period of investment.
Chain Rule
A method used to solve problems involving multiple proportional relationships by comparing a unknown quantity to a known chain of ratios.
Important Formulas
Board Exam Info
In the Maharashtra (MSBSHSE) Class 8 Mathematics examination, this chapter typically carries around 6 to 8 marks. Common question types include word problems based on direct and inverse variation (like finding the number of workers required for a job), partnership profit distribution sums, and multi-step proportional reasoning word problems.
Frequently Asked Questions
How do I know whether a word problem is direct or inverse variation?
Ask yourself: If one quantity increases, does the other also increase? If yes, it is direct variation (e.g., more items cost more money). If one increases and the other decreases, it is inverse variation (e.g., more workers take less time to complete a job).
What is the value of 'k' and how do I find it?
The letter 'k' represents the constant of variation. You can find it by dividing the two given values in direct variation (k = x/y) or by multiplying them in inverse variation (k = x × y).
How are profits divided in a business partnership?
Profits are divided in the ratio of the product of the capital invested by each partner and the duration (time) for which the capital was invested.
Learn Proportional Reasoning-2 with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards