Two quantities may change in such a way that one quantity may increase (or decrease) with the decrease (or increase) of the other quantity. Then the two quantities are said to be in inverse proportion or one quantity is inversely proportional to the other. For example, if we take more number of workers then our work will get done soon. It means that, number of workers is inversely proportional to the number of days the work can be done in.
Also, if we increase the speed of the car, the time taken to reach the destination decreases. Here, the speed of the car is inversely proportional to time.
Mathematically the inverse proportion is defined as follows.
Two quantities a and b are said to be inversely proportional to each other if
a = k/b where k is a constant.
i.e. ab =k
If a1, a2 are the values of a and b1, b2 are the values of b then the above equation can be re-written as
a1b1 = k and a2b2 = k
So, a1b1 = a2b2
This relation is mostly used in solving the mathematical problems with inverse proportion.
Example:
8 pipes are required to fill a tank within 30 minutes. How long the tank will take to be filled if there are 6 pipes.
Solution:
Here, we need to observe that it will take more time if the number of pipes is reduced to fill the tank.
So, the number of pipes and the time are in the inverse proportion.
| Number of pipes | Time (in minutes) |
| 8(a1) | 30 (b1) |
| 6 (a2) | x (b2) |
We have, a1b1 = a2b2
8 * 30 = 6 x
240 = 6x
Dividing both sides by 6,
x = 240/6 = 40
So, the tank requires 40 minutes to be filled.
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