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