Confused between Direct and Indirect Variation? Get clarity now!! We are providing detailed information and also the introduction to indirect proportion here. Direct Variation defines a linear relationship between 2 variables, inverse proportion defines another kind of relationship. Inversely proportion relationship will be described in longer form. Know every detail of Indirect Proportion or Variation here. Check the below sections to know all the information.
Inverse Variation
Mathematics is one of those subjects where you require problem solving and time management skills. With the given tips, you can easily make these possible to solve all the questions in given time. Ratios are the mathematical relationships which we use in the real world. These are explained based on fractions. If the fraction is represented as x:y, they are said to be in proportion which also states that 2 ratios are equal.
If we go with the example explanation, Suppose that we are constructing a bridge or a house, then the no. of days it takes to complete the building depends on the number of workers. Suppose we want to complete a house in less no. of days, then more number of workers are required. So, the no. of days is inversely proportional to no. of workers.
No. of days = 1/No. of Workers
Some of the examples in our day to day life also vary inversely. Some of these are in a stringed instrument, the frequency of vibration does vary inversely with the string length. The gravitational force between any two bodies would be inversely proprtional to power 2 of the distance.
If you are preparing for some of the competitive exams or bank exams, then you must definitely be perfect in all the topics and ratios and proportions. Most of the students will be confused between direct variation and indirect variation. So, you can check the example problems here to clear your confusion.
Definition of Inverse Variation
The mathematical expression or relationship between two variables that expresses by an equation in which the product of two quantities is equal to a constant value.
Sometimes, we notice that the variation in 1 value of one quantity differs or just opposite to the variation in another or second value. i.e. If the value of one quantity increases, the value of the another quantity decreases in the equal proportion and vice versa. In this case, two quantities are said to be inversely proportional.
Books for Inverse Variation
- On the Law of Inverse Variation of Extension and Intension by Richard Milton Martin
- Exam Prep for Thinking with Mathematical Models; Linear & Inverse Proportions by David Mason
- Regularization of Inverse Problems by Heinz Werner Engl, Martin Hanke, A. Neubauer
- Experimental Study Regarding Variation of Force in Inverse Proportions by Elsevier Limited
- Thinking with Mathematical Models: Linear and Inverse Variation by Glenda Lappan
- Fundamentals of Math Book 2: Algebra – Book 2 by Jerry Ortner
- Inverse Problems, Image Analysis, and Medical Imaging by Jerry Zuhair Spinelli
- New Mathematics Today by ANUBHUTI GANGAL
How to solve Inverse Variation Problems?
Step 1: Read the question once or twice carefully. The equation to solve Inverse Proportion is y=k/x. While solving word problems, use variables other than x, y. Use the variables which are relevant to the question or problem that is to be solved. Also, check the question carefully to know the inverse equations like squares, cubes, and square roots.
Step 2: Use the information given in the question to find the value of k. The constant value k is called constant of proportionality or constant of variation.
Step 3: Rewrite the formed equation from step 1 by substituting the values of k in the equation of step 2.
Step 4: Use the equation from step 3 and complete solving the remaining problem with the instructions given in the question.
Step 5: Do not forget to include the units at the end of the solution and also re-check the solution to avoid calculation mistakes.
Solved Example Questions
Question 1:
3 pipes take 60 minutes to water the field. How much time will it take to water the field with 6 pipes?
Solution:
Read the problem carefully
First, find out whether it is a directly proportional question or an inversely proportional question.
As more pipes are there, time reduces.
Hence pipes and minutes are inversely proprtional.
Here, we can write it as 3 pipes * 60 minutes = 6 pipes * n minutes
From the above equation, n = 30 minutes.
This is the mathematical representation of the given problem.
You can solve it even in a different way
Given for 3 pipes and asked to find for 6 pipes. It means the number of pipes is doubled. So, time will be reduced to half, that is 30 minutes.
Question 2:
4 friends consume 16kgs of rice in a month. The same amount of rice lasted for 20 days when a few more friends joined. How many additional members joined the group?
Solution:
It is given in the question that, 4 friends need 30 days to consume rice.
If rice is consumed within 20 days, how many additional friends are joined is the thing we need to find, let’s assume it to be x.
This a problem of inverse variation.
4 friends * 30 days = x friends * 20 days
From the above equation, x = 6.
So from the above solution, 6 friends need 20 days to consume 16kg of rice.
The number of additional members required to consume 16kgs of rice in 20 days is 2.
Question 3:
y varies inversely with the square of x. When x=2, y=10. Find x when y=20?
Solution:
In order to solve the above equation, we can translate the above sentence into a simple mathematical equation
y=k/(x^2). This implies y varies inversely with square of x by some constant.
Given x=2, y=3
Inverse Variation Equation is y=k/x2
10=k/22
10=k/4
y=40/x2
y=40x-2
20=40/x2
20x2/20=40/20
x2 = 2
x=+-root(2)
We have provided all the details regarding inverse proportion here. Prepare all the topics and concepts from ratios and proportions. Stay tuned to our website for all the stunning updates. We wish you all the best for your future.