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