# Inverse Proportion Formula

Before learning the inverse proportion formula, let us recall what is an inverse proportional relation. When two quantities are related to each other inversely, i.e., when an increase in one quantity brings a decrease in the other and vice versa then they are said to be inversely proportional. Inverse proportion formulas help in establishing a relationship between two inversely proportional quantities. Let us learn about the inverse proportion formula with a few solved examples in the end.

## What Is Inverse Proportion Formula?

Let x and y be two quantities and assume that x is decreasing when y is increasing and vice versa. Examples: The height is inversely proportional to the temperature. As the height increases, the temperature decreases. Taking height as x and temperature as y, we can say that y is said to be inversely proportional to x and is written mathematically as inverse proportion formula.

Here the symbol ∝ denotes the proportional relationship between two quantities.

### Inverse Proportion Formula

The inverse proportional formula is written as

**y =k/x**

where

- k is the constant of proportionality.
- y increases as x decreases.
- y decreases as x increases.

Let us learn the inverse proportion formula along with a few solved examples.

## Examples on Inverse Proportion Formula

**Example 1:** Suppose x and y are in an inverse proportion such that, when x = 120, then y = 5. Find the value of y when x = 150 using the inverse proportion formula.

**Solution: **

To find: Value of y

Given: x = 120 when y = 5

x ∝ 1/y

x = k / y, where k is a constant

or k = xy

Putting, x = 120 and y = 5, we get;

k = 120 × 5 = 600

Now, when x = 150, then;

150 y = 600

y = 600/150 = 4

That means when x is increased to 150 then y decreases to 4.

**Answer: **y = 4, when x = 150

**Example 2:** The time taken by a vehicle is 3 hours at a speed of 60 miles/hour. What would be the speed taken to cover the same distance at 4 hours?

**Solution:**

To find: The value of speed

Consider speed as m and time parameter as n.

If the time taken increases, then the speed decreases. This is an inverse proportional relation. m ∝ 1/n

Using the inverse proportion formula,

∴ m = k/ n

m × n^{ }= k

At speed of 60miles/hour, time = 3 hours from 1st condition we get,

k = 60 × 3 = 180

Now, we need to find speed when time = 4

m × n^{ }= k

m × 4^{ }= 180

∴ m = 180/4 = 45

**Answer: **Speed at 4 hours is 45 miles/hour

**Example 3: **In a construction company, a supervisor claims that 7 men can complete a task in 42 days. In how many days will 14 men finish the same task?

**Solution:**

Consider the number of men be M and the number of days be D

Given: \(M_1\)= 7 , \(D_1\) = 42, and \(M_2\) = 14

This is an inverse proportional relation, as the number of workers increases, the number of days decreases.

M ∝ 1/D

considering the first situation, \(M_1\) = k/ \(D_1\)

7 = k/42

k = 7 × 42 = 294

considering the second situation, \(M_2\) = k/ \(D_2\)

14 = 294/ \(D_2\)

\(D_2\) = 294/14 = 21

**Answer: ****It will take 21 days for 14 men to do the same task.**

## FAQs on Inverse Proportion Formula

### What Is the Symbol ∝ Denotes in Inverse Proportion Formula?

In the inverse proportion formula, the proportionate symbol ∝ denotes the relationship between two quantities. It is expressed as x ∝ 1/y. This implies x = k/y, where k is the constant of proportionality.

### How do you Represent the Inverse Proportional Formula?

The inverse proportional formula depicts the relationship between two quantities can be understood by the formula given below:

- Identify the two quantities which vary in the given problem.
- Identify that there is an inverse variation. x ∝ 1/y
- Apply the Inverse proportion formula x = k/y

### How To Show Relationship Between Two Quantities Using Inverse Proportion Formula?

The inverse proportional relationship between two quantities can be shown if the product of two quantities (x × y) is constant, then they depict an inversely proportional relationship. It is expressed as x ∝ 1/y. x = k/y, where k is the constant of proportionality.