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?
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.
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,
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?
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.