Inverse Variation Formula
Inverse variation formula exists between any two variables when one quantity is inversely dependent on the other i.e., if one quantity increases, the other quantity decreases, and vice versa. Since the two variables are inversely related to each other it is also termed as inversely proportional. The ratio of these two variables is always a constant number. Let's look into the mathematical representation of the inverse variation formula.
What is Inverse Variation Formula?
Let's consider two variables x and y. If the quantity y is inversely varying with respect to the quantity x i.e, y ∝ 1/x, then the inverse variation formula is given by,
y = (1/k) x OR y = x/k
where,
k is the constant of proportionality
Let's say \(y_1\) inversely varies with \(x_1\) and \(y_2\) inversely varies with \(x_2\) then, the inverse variation formula is given by
\(x_1y_1 = x_2y_2\)
Below is the graph is shown for the inverse variation relationship between x and y.
Let us now solve some problems on the inverse variation formula.
Solved Examples Using Inverse Variation Formula

Example 1: Suppose x and y are in an inverse proportion such that, when x = 15, then y = 4. Find the value of y when x = 20.
Solution:
Given: \(x_1\) = 15, \(y_1\) = 4, \(x_2\) = 20, \(y_2\) = ?
Using inverse variation formula,
\(x_1y_1 = x_2y_2\)
⇒ 15 × 4 = 20 × \(y_2\)
⇒ 60 = 20 × \(y_2\)
⇒ \(y_2\) = 3
Answer: Thus, the value of y is 3, when x is 20.

Example 2: 12 pipes are required to fill a tank in 5 hours. How long will it take if 10 pipes of the same type are used?
Solution:
Let, the desired time to fill the tank be x minutes.
We know that as the number of pipes increases, the time taken to fill the tank will decrease.
Hence, this is a case of inverse variation. Thus, the number of pipes is inversely proportional to the time taken.
Using inverse variation formula,
\(x_1y_1 = x_2y_2\)
\(x_1\) = 12, \(y_1\) = 5 , \(x_2\) = ?, \(y_2\) = 10
⇒ 12 × 5 = \(x_2\) × 10
⇒ \(x_2\)_{ }= 6 hours
Answer: Thus, it will take 6 hours for 10 pipes.