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, x_{1} = 20, x_{2} = 45 and y_{1} = 15 .

By the product rule of inverse variation,

(20)(15) = (45)(y_{2})

300 = 45y_{2}

y_{2} = 300/45 = 20/3

Therefore, 45 men can do the same job in 20/3 days.