Question

divide 20 into 4 parts which form an ap such that the product of 1st and 4th term bears a ratio to the product of 2nd and 3rd term as 2:3

Answer 1

let the numbers be x - 3d, x - d, x + d, x + 3d.
Adding all, we get 4x = 20. x = 5.
3*(x-3d)*(x+3d) = 2*(x-d)*(x+d)
3x^2 - 27d^2 = 2x^2 - 2d^2
x^2 = 25d^2
25 = 25 d^2
d ^ 2 = 1
d = 1
Therefore the numbers are 5 - 3(1) , 5 - 1, 5 + 1, 5 + 3(1)
ie, 2,4,6,8

Answer 2

the answer is 2,4,6,8