Inversely proportional

In Mathematics as well as in Physics, we learn about quantities. Some quantities depend upon one another, and such quantities are termed as proportional to one another. In other words, two variables are said to be proportional to each other, if one is changed, then the other is also changed by a fixed amount. This property of variables is known as proportionality. The symbol used to represent the proportionality is “∝.” There are two types of proportionality of variables. They are

  • Directly Proportional
  • Inversely Proportional

Direct and Inverse proportion

Inversely Proportional Meaning

Directly proportional variables are those in which if one variable increases, the other also increases. If one variable decreases, the other decreases in the same proportion. Inversely proportional variables are those in which one variable decreases with the increase in another variable and one variable increases with the decrease in another variable. It is opposite to direct proportion. Two quantities are said to be inversely proportional when one quantity is in direct proportion to the reciprocal of others.

Inversely Proportional Definition

Two variables are called inversely proportional, if and only if the variables are directly proportional to the reciprocal of each other. Inversely proportional is also called an inverse variation or reciprocal proportion.

Inversely Proportional Equation

If x and y are two quantities which are in inverse variations, then

x ∝ 1/y

x = k(1/y)

Where “k” is a universally positive constant

It can also be represented as xy = k

If x and y are in inverse variation and x has two values x1 and x2 corresponding to y having two values y1 and y2 respectively, then by the definition of inverse variation, we have

x1 y1 = x2 y2 = (k)

In this case, it becomes

x1 / x2 = y2 / y1 = k

Inversely Proportional Example

Question: Find A when B = 500, if A is inversely proportional to B, and also given that A = 200, B = 0.6.

Solution:

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 = 200 and B = 0.6

So, k = 200 x 0.6 = 120

Therefore, k = 120.

From the above equation, we get

k = 120

Now, substitute the value of k to find A

120 = A x 500

A = (120)/(500) = 0.24

Therefore, A = 0.24

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