Situations of Inverse Variation

We will learn ‘what inverse variation is’ and how to solve different types of problems on some situations of inverse variation.

If two quantities are related in such a way that increase in one quantity causes corresponding decrease in the other quantity and vice versa, then such a variation is called an inverse variation or indirect variation.

If the two quantities are in inverse variation then we say that they are inversely proportional.

Suppose, if two quantities x and y vary inversely with each other, then the values of x is equal to the inverse ratio of the corresponding values of y.

i.e., \(\frac{x_{1}}{x_{2}} = \frac{y_{2}}{y_{1}}\)

or, \(x_{1} \times y_{1} = x_{2} \times y_{2}\)


Some situations of inverse variation:

● More men at work, less time taken to finish the work.

Less men at work, more time is taken to finish the work.

● More speed, less time is taken to cover the same distance.

Less speed, more time is taken to cover the same distance.                   


Problems on different situations of inverse variation:

1. If 48 men can do a piece of work in 24 days, in how many days will 36 men complete the same work?

Solution: 

This is a situation of indirect variation.

Less men will require more days to complete the work.

48 men can do the work in 24 days

1 man can do the same work in 48 × 24 days

36 men can do the same work in (48 × 24)/36 = 32 days

Therefore, 36 men can do the same work in 32 days.


2. 100 soldiers in a fort had enough food for 20 days. After 2 days, 20 more soldiers join the fort. How long will the remaining food last?

Solution:

More soldiers, therefore, food lasts for less days.

This is a situation of indirect variation.               

Since 20 soldiers join the fort after 2 days, therefore, the remaining food  is sufficient for 100 soldiers and 18 days.

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method





7th Grade Math Problems

From Situations of Inverse Variation to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

    Feb 28, 24 04:07 PM

    Fraction 8/16
    There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

    Read More

  2. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 28, 24 01:43 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More

  3. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 27, 24 02:43 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  4. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  5. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion