Question

Divide 28 into four parts in an A.P. so that the ratio of the product of first and third with the product of second and fourth is 8:15.

Answer 1

Correct Answer - 4, 6, 8, 10
Let four member be a-3d,a-d,a+b,a+3d.
Here, 4a=28 or a=7
Also, `((a-3d)(a+d))/((a-d)(a+3d))=8/15`
or `15[a^(2)-3d^(2)-2ad]=8[a^(2)-3d^(2)+2ad]`
or `7(a^(2)-3d^(2))=46ad`
or `7(49-3d^(2))=46xx7xxd`
or `49-3d^(2)=46d`
`3d^(2)+46d-49=0`
or (d-1)(3d+49)=0
or d=1
Therefore, the required numbers are 4, 6, 8, 10.