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WORD PROBLEMS INVOLVING INVERSE PROPORTIONS

Direct and inverse proportions of Class 8

Inverse proportionality is exactly opposite to directly proportions i.e. two variables are said to be inversely proportional if an increase in value of one variable results in a decrease in value of the other variable and similarly a decrease in value of one variable results in an increase in value of the other variable. The questions are also of the form, "If x results in a, what will be the result if  x changes to y?

You need a simple 4 step approach to solve the problems:

  • Identify Variables: Usually this is a simpler thing to do. The variables are fairly obvious in typical proportion problems.
  • Understand the Relationship: Is the relationship between variables inversely proportional? Understand the context and use common sense. For example the following relationships are inversely proportional
  • The time a car needs to travel between two towns is inversely proportional to its speed i.e. higher the speed the less time it takes to cover the same distance
  • The time it takes to do a job is inversely proportional to the number of people employed to do the job i.e. if it takes 4 men to complete a wall in 2 days, 8 men can do the same job in 1 day.
  • Express the proportionality: Get the problem to a form: "If x results in a, what will be the result if  x changes to y?"

question 1. A car takes 1 hour and 30 minutes to travel the distance between two cities during rush hour. If the average speed is 50% more during off-peak hours, what time will it take to cover the same distance between the two cities during off peak hours (1 hour = 60 minutes)?

(a) 45 Minutes (b) 1 Hour (c) 1 Hour 15 Minutes

(d) 90 Minutes (e) 1 Hour 45 minutes

Solution: Step 1: The time taken to cover the distance and the speed are inversely proportional. Let the speed during rush hour be 8. 

The average speed is 50% more during off-peak hours therefore off-peak hour speed = 1.5s

Step 2: With speed s it takes 1 hour 30 minutes = 1 × 60 + 30 = 90 minutes

Since the speed and time are inversely proportional, the time taken with speed WORD PROBLEMS INVOLVING INVERSE PROPORTIONS Minutes or 1 Hour

The correct answer is B

CBSE NCERT Solutions for Class 8 Maths

class 8 maths NCERT solutions Chapter 1: Rational Numbers

class 8 maths NCERT solutions  Chapter 2: Linear Equations in One Variable

class 8 maths NCERT solutions  Chapter 3: Understanding Quadrilaterals

class 8 maths NCERT solutions Chapter 4: Practical Geometry

class 8 maths NCERT solutions  Chapter 5: Data Handling

class 8 maths NCERT solutions  Chapter 6: Square and Square Roots

class 8 maths NCERT solutions  Chapter 7: Cube and Cube Roots

class 8 maths NCERT solutions  Chapter 8: Comparing Quantities

NCERT Class 8 Maths solution Chapter 9: Algebraic Expressions and Identities

class 8 maths NCERT solutions  Chapter 10: Visualizing Solid Shapes

class 8 maths NCERT solutions Chapter 11: Mensuration

class 8 maths NCERT solutions  Chapter 12: Exponents and Powers

class 8 maths NCERT solutions  Chapter 13: Direct and Inverse Proportions

class 8 maths NCERT solutions  Chapter 14: Factorization

class 8 maths NCERT solutions  Chapter 15: Introduction to Graphs

class 8 maths NCERT solutions  Chapter 16: Playing with Numbers

 

Notes,worksheet and solved question for Maths class 8 

  1.  class 8 maths notes on chapter Liner equation in one variable
  2. class 8 maths notes on chapter algebric expression 
  3. class 8 maths notes on chapter Mensuration 
  4. class 8 maths notes on chapter Square and square roots 
  5. class 8 maths notes on chapter statistice
  6. class 8 maths notes on chapter practical Geometry
  7. class 8 maths notes on chapter commericial maths
  8. class 8 maths notes on chapter solid shape
  9. class 8 maths notes on chapter quadrilaterals
  10. class 8 maths notes on chapter exponents
  11. class 8 maths notes on chapter factorisation 
  12. class 8 maths notes on chapter inverse proporation 
  13. class 8 maths notes on chapter cube and cube roots 

Check your marks in a chapter which you have complited in school from Physics Wallah chapter wise online test just click on the link given below

chapter wise online test for class 8 maths 

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