Inverse Proportion

Introduction:

Inversely proportion is the proportionality that decreases one quantity when another quantity is increased or increases one quantity when another quantity is decreased. It is opposite to direct proportionality. Two quantities are said to be inverse when one quantity is directly proportion to the reciprocal of other.

If two quantities A and B are inversely proportion then they are generally represented as:

A ? 1/B (or) A ? B^-1

And these two quantities are equivalent when a constant k is introduced. And it is written as.

A=k (1/B) (or) A=k/B

Where,

k=universal constant.

Here A and B are inversely proportion if when A changes then B changes reciprocally to A.

Example:

Let us assume a guy has traveled 50 kmph in an hour and after taking few minutes break he has traveled 25 kmph in 2 hours.

Here the change in hours will change the average speed that he has traveled. So here the change in hours factored by 2(i.e. changed from 1 to 2) and the change in speed is factored by 1/2(i.e. changed from 50 to 25).

In the above example the time is inversely proportional to the average speed. Because when the time is doubled the average speed is made into half.

Graph between A and B when they are inverse:

The graph looks like a curve which slightly falls down.

Properties:

?When two quantities are inversely proportion then their values should be reciprocal.

?The product of two quantities is always equal to the constant.(i.e. AB=k)

?The increase in one quantity decreases the other and vice versa.

Solved problems

1)In a committee there are 6 people the probability of any one to become the chairman is?

Given data:

Total no. of people in a committee= 6

The probability of any one to become the chairman=1/6.

Here the probability is inversely proportional to committee members.

2)Find A when B=300, If A is inversely proportional to B and A=150 B=0.5?

Given,

Here A is inversely proportional to B i.e.

A=k (1/B)

Where k is a constant and we get k=A x B

Given that A=150 and B=0.5

We get k=150 x 0.5=75

There fore k=75.

k=A x B

From above equation k=75

75=A x 300

Therefore A=75/300=0.25