Inverse Proportion

Chapter 13 Class 8 Direct and Inverse Proportions
Concept wise

Inverse proportion means

When one quantity increases, the other quantity decreases

Example

• If speed increases, time taken decreases
• If number workers doing a job increase, the total time to complete a job decreases

So, we can say that

Speed and Time are inversely proportional

Similarly,

Number of workers and total time are inversely proportional

How to solve questions with Inverse Proportion?

Let’s take an example

Suppose at 50 km/hr, it takes us 4 hours to reach a destination. How much time would it take to reach a destination if speed is 100 km/hr?

Given that,

It takes 4 hours to reach destination at speed of 50 km/hr

We need to find how much time would it take if speed is 100 km/hr

Let the time taken be x hours

Now, we draw a table

 Time (in hours) 4 x Speed (in km/ hr ) 50 100

Now, as speed increases

time taken will decreases

So, Time and Speed are in inverse proportion

So, we write numbers as

x 1 y 1 = x 2 y 2

So,

x 1 y 1 = x 2 y 2

4 × 50 = x  × 100

(4 × 50)/100 = x

4/2 = x

2 = x

x = 2

So, it takes 2 hours to travel

Let’s take another example

Suppose 5 workers complete a job in 10 days. How much time would it take if there are 10 workers?

Given that,

5 workers complete a job in 10 days

We need to find much time would it take if there are 10 workers

Let the time taken be y days

Now, we draw a table

 Number of workers 5 10 Time taken (days) 10 y

Now, as number of workers increases,

time taken to complete the job will decrease

So, they are in inverse proportion

So, we write numbers as

x 1 y 1 = x 2 y 2

5 × 10 = 10 × y

(5 × 10)/10=y

5 = y

y = 5

So, it will take 5 days

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