<PRE><B>Question 852499</B>
three numbers in ratio 2:5:8
let these numbers are  2x:5x:8x
as per given conditions if 10 is added to middle number
number forms GP(if a,b,c are GP than b^2=ac)
2x,5x+10,8x
(5x+10)^2=2x multiplied by 8x
25x^2+100x+100=16x^2
9x^2+100x+100=0
9x^2+90x+10x+100=0
9x(x+10)+10(x+10)=0
(x+10)(9x+10)=0
x=-10 or x=-10/9
neglecting n second value as it can not be fractional  we consider x=-10
numbers are 2x:5x:8x
          =-20:-50:-80
verification
(-50+10)^2= -20 multiplied by -80
1600=1600
verified </PRE>