Three numbers are in GP whose sum is 70 . if the extremes be each multiplied by 4 and mean by 5 , they will be in AP . find the numbers.

Answers (1)

Solution:    Let the three numbers in GP be  fracar,a,ar

 Given    ,                 fracar+a+ar=70

and    frac4ar,5a,4ar  are in AP.

 	herefore                              10a=frac4ar+4arRightarrow frac10a4=fracar+ar

  or                                 frac5a2=70-a          From  Eq.(1)

    or                             5a=140-2aRightarrow a=20.

     From Equation (1)  , we get 

                                      frac20r+20+20r=70   or    frac20r+20r=50

   Rightarrow                           2r^2-5r+2=0Rightarrow (r-2)(2r-1)=0

   	herefore                                           r=2,frac12

   Hence , the three numbers are 10,20,40  or      40,20,10.            

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