 # Inverse Variation Formula

Inverse variation formula refers to the relationship of two variables in which a variable increases in its value, the other variable decreases and vice-versa. In other words, the inverse variation is the mathematical expression of the relationship between two variables whose product is a constant.

## Formula for Inverse Variable

The Inverse Variation Formula is,

 y ∝ (1 ⁄ x) ⇒ y = (k ⁄ x)

Here, K is the constant of proportionality.

### Solved Example Question

Question 1: If y varies inversely with x and when y = 100, x = 30. What is the value of y when x = 10?

Solution:

Given, y = 100 x = 30

The inverse variation formula is,

y = (k ⁄ x)

100 = (k ⁄ 30)

k = 100 × 30

k = 3000

Now, x = 10 k = 3000

y = (k ⁄ x)

y = (3000 ⁄ 10)

y = 300

Question 2: Suppose that y varies inversely as x when x = 10 and y = 12/5. Find the value of x when y = 8.
Solution:
Given,
x = 10, y = 12/5
The inverse variation formula is:
y = k/x
xy = k
Therefore, k = (10) × (12/5) = 24
Now, substitute the values of y and k in the equation xy = k,
Thus,
x(8) = 24
x = 24/8 = 3
Hence, the value of x = 3.

Question 3: In a manufacturing company, 20 men can do the job in 15 days. How many days will it take if 45 men do the same job?
Solution:
Here, when the manpower increases, they will need less than 15 days to complete the same job. So, this is an inverse variation.
Let x be the number of men workers and let y be the number of days to complete the work.
So, x1 = 20,  x2 = 45 and y1 = 15 .
By the product rule of inverse variation,
(20)(15) = (45)(y2)
300 = 45y2
y2 = 300/45 = 20/3
Therefore, 45 men can do the same job in 20/3 days.