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Home > Maths II > Relationships > Variation

Maths II


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Inverse Variation

In an inverse variation (proportion), the values of the two variables change in an opposite manner - as one value increases, the other decreases.

Inverse proportion is described in the language of variation as follows -

  • P varies inversely as Q
  • P is inversely proportional to Q
  • P \propto {1 \over Q} (read as P varies inversely as Q)
  • P = {k \over Q} , where k is the constant of variation


For example, the number of days required to build a bridge varies inversely to the number of workers. As the number of workers increases, the number of days required to build would decrease.


y varies inversely as x, and y = 10 when x = 2.

  • (a) Find a formula connecting y and x
  • (b) Determine y when x = 4
  • (c) Determine x when y = 40



(a) y \propto {1 \over x} \rightarrow y = {k \over x}

(b) Find the value of k: 10 = {k \over 2}, so k = 20

   Using the formula, and constant k, find the missing value of y when x = 4:


   y = {20 \over x}


   y = {20 \over 4}


   y = 5


(c) y = {k \over x}


      40 = {20 \over x}


      x = {20 \over 40}


      x = {1 \over 2}

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