Solved Examples on Constant of Proportionality

Example 1: You are in the market for pencils, and you observe that for every 4 pencils you purchase, it costs you Rs 8. What is the Constant of Proportionality?

Solution:

In this scenario, ‘x’ denotes the quantity of pencils (4) and ‘y’ signifies the cost (Rs 8)

By utilising the equation y = kx, we can determine ‘k’

k = y/x = 8/4 = 2

Therefore, the Constant of Proportionality (‘k’) is 2.

Example 2: If the expense for 3 hamburgers amounts to Rs 12 then compute the Constant of Proportionality.

Solution:

In this situation, ‘x’ represents the number of hamburgers (3) and ‘y’ is the cost (Rs 12) and we have to find ‘k’ the constant of proportionality

By using the equation y = kx,

we can calculate ‘k’ as follows:

k = y/x = 12/3 = 4

Hence, the Constant of Proportionality ‘k’ equals to 4.

Example 3: Suppose you are shopping for notebooks and you realize that for every 5 notebooks you purchase, it costs you Rs 20. What is the Constant of Proportionality in this case?

Solution:

Here, ‘x’ corresponds to the number of notebooks (5) and ‘y’ denotes the cost (Rs 20), and we want to find ‘k.’

By using the equation y = kx,

we can calculate ‘k’ by reordering it:

k = y/x = 20/5 = 4.

Thus, the Constant of Proportionality ‘k’ is 4.

Example 4: Now, let’s consider a scenario where you are purchasing movie tickets. You notice that for every 2 tickets you buy, it costs you Rs 300. Can you determine the Constant of Proportionality?

Solution:

In this situation, ‘x’ represents the number of movie tickets (2) and ‘y’ signifies the cost (Rs 300) and we aim to find ‘k.’

Employing the equation y = kx

we can calculate ‘k’ as follows:

k = y/x = 300/2 = 150.

Thus, the Constant of Proportionality ‘k’ is 50.

Constant of Proportionality is a fundamental concept in mathematics that helps us understand the relationships between two varying quantities. Constant of Proportionality is used for analyzing direct and inverse relationships in various contexts. Constant of Proportionality represents the unchanging value in the ratio between two directly or inversely proportional quantities.

Constant of Proportionality is often denoted as ‘k’ that relates two directly or inversely proportional quantities. In this article, we will discuss the Constant of Proportionality in detail including its definition and types. We will also have a look at various solved examples on the Constant of Proportionality concept for understanding.