# 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 Minutes or 1 Hour

The correct answer is B

CBSE NCERT Solutions for Class 8 Maths

Notes,worksheet and solved question for Maths class 8

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