Direct Variation


When two quantities are said to be in direct variation if one quantity increases,then the other also increases or when one quantity decreases,the other also decreases.

Where we use this method:

5 books costs $125. 8 books at the same rate cost $200 and 2 books cost $50.This example shows that more number of books cost more money and less number of books cost less money.Here number of books and cost of books are in direct variation.

Practical examples :

  • Principal and interest at constant rate of interest and period.
  • Time and interest for the same principal at the same rate of interest.
  • Speed and distance covered.
  • Men and amount of work.
  • Time and distance at constant speed.

To understand this topic more clearly we have given two problems.

Example 1:

Cost of 25 books is $ 600.What is the cost of 47 books?


            Number of books                         Cost of books  

                   25  -------------------------   600

                   47  -------------------------     x

The more number of books,the cost of books will also be more.We need to solve for x from here to know the cost of 47 books.

For applying this concept we need to cross multiply the details.

                              25 x X  =  600 x 47

                                     X  = (600 x 47) / 25

                                         = $ 1128

Example 2:

Mr.Alex deposited $4000 in a bank and earned $2500 as interest for a certain period.If he had deposited $ 15000 for the same period.What would have been his interest?


                    Amount                                            Interest  

                   4000   -----------------------     2500

                   15000  -----------------------      x

Here amount invested by Alex is increasing from 4000 to 15000.So obviously the interest will become high.To solve for x we need to cross multiply.

                             4000 x X  =  15000 x 2500

                                       X  = (15000 x 2500) / 4000

                                           = $ 9375

 We can easily say from the above picture as the temperature increases,  the number of people buying ice cream will also increase.

        Students can try to solve the above examples on their own, and verify with the given solution.  If you are having any doubt you can contact us through mail, we will help you to clear your doubts.

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Direct variation to Basic math

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